data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 2
values | reward_model dict | extra_info dict |
|---|---|---|---|---|
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 133,
"split": "train",
"text": "Cobra Mist\n\nFrom Wikipedia, the free encyclopedia\nJump to: navigation, search\nThe former Cobra Mist building in October 2004\n\nCobra Mist was the codename for an Anglo-American experimental over-the-horizon radar station at Orford Nes... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 133,
"split": "train",
"text": "Cobra Mist\n\nFrom Wikipedia, the free encyclopedia\nJump to: navigation, search\nThe former Cobra Mist building in October 2004\n\nCobra Mist was the codename for an Anglo-American experimental over-the-horizon radar station at Orford Nes... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 134,
"split": "train",
"text": "# How to Calculate Doubling Time\n\n## Three Methods: Calculate Growth Rate, Calculate Doubling Time, Calculate Population Doubling Level (PDL) Period\n\nDoubling time refers to the time it takes for the growth of specific things to double, su... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 134,
"split": "train",
"text": "# How to Calculate Doubling Time\n\n## Three Methods: Calculate Growth Rate, Calculate Doubling Time, Calculate Population Doubling Level (PDL) Period\n\nDoubling time refers to the time it takes for the growth of specific things to double, su... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 134,
"split": "train",
"text": "# How to Calculate Doubling Time\n\n## Three Methods: Calculate Growth Rate, Calculate Doubling Time, Calculate Population Doubling Level (PDL) Period\n\nDoubling time refers to the time it takes for the growth of specific things to double, su... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 135,
"split": "train",
"text": "Take the 2-minute tour ×\n\nI have to solve a problem in the field of operations research. I want to gather some general approaches to evaluate them to pick the most promising to design a problem-related program.\n\nProblem definition\n\nC... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 135,
"split": "train",
"text": "Take the 2-minute tour ×\n\nI have to solve a problem in the field of operations research. I want to gather some general approaches to evaluate them to pick the most promising to design a problem-related program.\n\nProblem definition\n\nC... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 135,
"split": "train",
"text": "Take the 2-minute tour ×\n\nI have to solve a problem in the field of operations research. I want to gather some general approaches to evaluate them to pick the most promising to design a problem-related program.\n\nProblem definition\n\nC... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 136,
"split": "train",
"text": "# Integrating Functions Involving Quadratic Expressions\n\n## Introduction\n\nIntegrals involving quadratic expressions of the form \\( a \\cdot x^2 + b \\cdot x + c \\) are often evaluated by completing the square. This method converts the ex... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 136,
"split": "train",
"text": "# Integrating Functions Involving Quadratic Expressions\n\n## Introduction\n\nIntegrals involving quadratic expressions of the form \\( a \\cdot x^2 + b \\cdot x + c \\) are often evaluated by completing the square. This method converts the ex... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "float",
"index": 136,
"split": "train",
"text": "# Integrating Functions Involving Quadratic Expressions\n\n## Introduction\n\nIntegrals involving quadratic expressions of the form \\( a \\cdot x^2 + b \\cdot x + c \\) are often evaluated by completing the square. This method converts the expr... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 137,
"split": "train",
"text": "\n\n (Source: CBS)\n\n\n\n\n\nMelting Prius owner\n\n\n\nStudio City\n\n\n\n\n\n[Image Source: Jason Mick/DailyTech]\n\n\nSource: CBS\n\nComments Threshold\n\n\nRE: Umm\nBy geddarkstorm on 1/26/2012 1:02:15 PM , Rating: 2\nYou just co... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 137,
"split": "train",
"text": "\n\n (Source: CBS)\n\n\n\n\n\nMelting Prius owner\n\n\n\nStudio City\n\n\n\n\n\n[Image Source: Jason Mick/DailyTech]\n\n\nSource: CBS\n\nComments Threshold\n\n\nRE: Umm\nBy geddarkstorm on 1/26/2012 1:02:15 PM , Rating: 2\nYou just co... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 137,
"split": "train",
"text": "\n\n (Source: CBS)\n\n\n\n\n\nMelting Prius owner\n\n\n\nStudio City\n\n\n\n\n\n[Image Source: Jason Mick/DailyTech]\n\n\nSource: CBS\n\nComments Threshold\n\n\nRE: Umm\nBy geddarkstorm on 1/26/2012 1:02:15 PM , Rating: 2\nYou just co... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 138,
"split": "train",
"text": "# Financial Calculations Using Excel: Future Value and Present Value\n\n## Questions\n\n1. **Future Value of Annuity and Present Value of a Security**\n\n 4.1 If you deposit $10,000 in a bank account that pays 10% interest annually, how much... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 138,
"split": "train",
"text": "# Financial Calculations Using Excel: Future Value and Present Value\n\n## Questions\n\n1. **Future Value of Annuity and Present Value of a Security**\n\n 4.1 If you deposit $10,000 in a bank account that pays 10% interest annually, how much... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 138,
"split": "train",
"text": "# Financial Calculations Using Excel: Future Value and Present Value\n\n## Questions\n\n1. **Future Value of Annuity and Present Value of a Security**\n\n 4.1 If you deposit $10,000 in a bank account that pays 10% interest annually, how much... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "float",
"index": 139,
"split": "train",
"text": "# Next Number in the Sequence\n\n## Introduction\nThis document explores the next number in a given sequence: 4, 8, 9, 10, 12, 16, 18, 20, 24, 25, 27, 28, ...\n\n## Discussion\n\n### Prime Factorization Approach\nAKG suggests analyzing the prime... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 139,
"split": "train",
"text": "# Next Number in the Sequence\n\n## Introduction\nThis document explores the next number in a given sequence: 4, 8, 9, 10, 12, 16, 18, 20, 24, 25, 27, 28, ...\n\n## Discussion\n\n### Prime Factorization Approach\nAKG suggests analyzing the pri... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 139,
"split": "train",
"text": "# Next Number in the Sequence\n\n## Introduction\nThis document explores the next number in a given sequence: 4, 8, 9, 10, 12, 16, 18, 20, 24, 25, 27, 28, ...\n\n## Discussion\n\n### Prime Factorization Approach\nAKG suggests analyzing the pri... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 140,
"split": "train",
"text": "# Homework Help: Physics\n\nPosted by Fatima on Sunday, January 22, 2012 at 11:47am.\n\nA 95 g tennis ball is traveling at 106 km/h when it bounces off a wall and travels in the opposite direction at a speed of 88 km/h.\n\n### Problem\n\na. De... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 140,
"split": "train",
"text": "# Homework Help: Physics\n\nPosted by Fatima on Sunday, January 22, 2012 at 11:47am.\n\nA 95 g tennis ball is traveling at 106 km/h when it bounces off a wall and travels in the opposite direction at a speed of 88 km/h.\n\n### Problem\n\na. De... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 140,
"split": "train",
"text": "# Homework Help: Physics\n\nPosted by Fatima on Sunday, January 22, 2012 at 11:47am.\n\nA 95 g tennis ball is traveling at 106 km/h when it bounces off a wall and travels in the opposite direction at a speed of 88 km/h.\n\n### Problem\n\na. De... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 141,
"split": "train",
"text": "# Understanding the Fundamental Theorem of Calculus\n\n## Introduction\n\nThe Fundamental Theorem of Calculus (FTC) is a central theorem in the field of calculus that links the concept of differentiation with that of integration. It consists o... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 141,
"split": "train",
"text": "# Understanding the Fundamental Theorem of Calculus\n\n## Introduction\n\nThe Fundamental Theorem of Calculus (FTC) is a central theorem in the field of calculus that links the concept of differentiation with that of integration. It consists o... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 141,
"split": "train",
"text": "# Understanding the Fundamental Theorem of Calculus\n\n## Introduction\n\nThe Fundamental Theorem of Calculus (FTC) is a central theorem in the field of calculus that links the concept of differentiation with that of integration. It consists o... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 142,
"split": "train",
"text": "# Differential Forms and the Generalized Stokes Theorem\n\n## Main Content\n\n### Introduction to Differential Forms\n\nDifferential forms are important concepts in mathematics with applications in physics, though they are not intuitive. In co... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 142,
"split": "train",
"text": "# Differential Forms and the Generalized Stokes Theorem\n\n## Main Content\n\n### Introduction to Differential Forms\n\nDifferential forms are important concepts in mathematics with applications in physics, though they are not intuitive. In co... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 142,
"split": "train",
"text": "# Differential Forms and the Generalized Stokes Theorem\n\n## Main Content\n\n### Introduction to Differential Forms\n\nDifferential forms are important concepts in mathematics with applications in physics, though they are not intuitive. In co... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 143,
"split": "train",
"text": "# Another Proof by Induction\n\n## Problem Statement\n\nWe need to prove that \n\n$$\\frac{1}{3}n^3 + \\frac{1}{2}n^2 + \\frac{1}{6}n$$ \n\nis an integer for all \\( n \\in \\mathbb{N} \\).\n\n## Proof\n\nFirst, we factorize the expression:\n\... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 143,
"split": "train",
"text": "# Another Proof by Induction\n\n## Problem Statement\n\nWe need to prove that \n\n$$\\frac{1}{3}n^3 + \\frac{1}{2}n^2 + \\frac{1}{6}n$$ \n\nis an integer for all \\( n \\in \\mathbb{N} \\).\n\n## Proof\n\nFirst, we factorize the expression:\n\... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "float",
"index": 143,
"split": "train",
"text": "# Another Proof by Induction\n\n## Problem Statement\n\nWe need to prove that \n\n$$\\frac{1}{3}n^3 + \\frac{1}{2}n^2 + \\frac{1}{6}n$$ \n\nis an integer for all \\( n \\in \\mathbb{N} \\).\n\n## Proof\n\nFirst, we factorize the expression:\n\n$... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 144,
"split": "train",
"text": "# My Sink Puzzle\n\n**Asked by unreality, July 26, 2007**\n\nThis is a water-measuring puzzle I made up. The challenge is to have exactly 7 oz of water in an 8-oz cup, using two 3-oz cups and one 8-oz cup, with the minimum amount of water wast... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 144,
"split": "train",
"text": "# My Sink Puzzle\n\n**Asked by unreality, July 26, 2007**\n\nThis is a water-measuring puzzle I made up. The challenge is to have exactly 7 oz of water in an 8-oz cup, using two 3-oz cups and one 8-oz cup, with the minimum amount of water wast... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 144,
"split": "train",
"text": "# My Sink Puzzle\n\n**Asked by unreality, July 26, 2007**\n\nThis is a water-measuring puzzle I made up. The challenge is to have exactly 7 oz of water in an 8-oz cup, using two 3-oz cups and one 8-oz cup, with the minimum amount of water wast... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 145,
"split": "train",
"text": "# Ordered Pair Solutions of Equations Video\n\n## Reviewer Rating\n\n**Assigned as a Homework Refresher**: This video serves as a refresher on the concept of ordered pairs as solutions to linear equations. Viewers observe how Sal uses the line... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 145,
"split": "train",
"text": "# Ordered Pair Solutions of Equations Video\n\n## Reviewer Rating\n\n**Assigned as a Homework Refresher**: This video serves as a refresher on the concept of ordered pairs as solutions to linear equations. Viewers observe how Sal uses the line... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 145,
"split": "train",
"text": "# Ordered Pair Solutions of Equations Video\n\n## Reviewer Rating\n\n**Assigned as a Homework Refresher**: This video serves as a refresher on the concept of ordered pairs as solutions to linear equations. Viewers observe how Sal uses the line... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 146,
"split": "train",
"text": "Howdy, Stranger!\n\n\n2010 Subaru Legacy 3.6 R\n\n\n\n • I have a new Legacy2010 - 3.6R was wondering if anyone has experienced any transmission slip issues when turning left or right? It does not seem to be an issue when going straight. ... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 146,
"split": "train",
"text": "Howdy, Stranger!\n\n\n2010 Subaru Legacy 3.6 R\n\n\n\n • I have a new Legacy2010 - 3.6R was wondering if anyone has experienced any transmission slip issues when turning left or right? It does not seem to be an issue when going straight. ... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 146,
"split": "train",
"text": "Howdy, Stranger!\n\n\n2010 Subaru Legacy 3.6 R\n\n\n\n • I have a new Legacy2010 - 3.6R was wondering if anyone has experienced any transmission slip issues when turning left or right? It does not seem to be an issue when going straight. ... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 147,
"split": "train",
"text": "Take the 2-minute tour ×\n\nFirst part of my question:\n\nI read on the ffmpeg documentation (section 3.2 How do I encode single pictures into movies?) the following:\n\nTo encode single pictures into movies, run the command:\n\n ffmpeg -... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 147,
"split": "train",
"text": "Take the 2-minute tour ×\n\nFirst part of my question:\n\nI read on the ffmpeg documentation (section 3.2 How do I encode single pictures into movies?) the following:\n\nTo encode single pictures into movies, run the command:\n\n ffmpeg -... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 147,
"split": "train",
"text": "Take the 2-minute tour ×\n\nFirst part of my question:\n\nI read on the ffmpeg documentation (section 3.2 How do I encode single pictures into movies?) the following:\n\nTo encode single pictures into movies, run the command:\n\n ffmpeg -... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 148,
"split": "train",
"text": "Take the 2-minute tour ×\n\nAs we know that the Object oriented programming language has lots of benefit.But in same implementation procedural language like C do not have any alternative like realtime applications. So can we combine the po... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 148,
"split": "train",
"text": "Take the 2-minute tour ×\n\nAs we know that the Object oriented programming language has lots of benefit.But in same implementation procedural language like C do not have any alternative like realtime applications. So can we combine the po... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 148,
"split": "train",
"text": "Take the 2-minute tour ×\n\nAs we know that the Object oriented programming language has lots of benefit.But in same implementation procedural language like C do not have any alternative like realtime applications. So can we combine the po... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 149,
"split": "train",
"text": "# Physics Concepts\n\n## Speed\nSpeed is the distance traveled by an object per unit of time. It is calculated as:\n\\[ \\text{speed} = \\frac{\\text{distance traveled}}{\\text{time}} \\]\n\n## Velocity\nVelocity is speed in a given direction;... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 149,
"split": "train",
"text": "# Physics Concepts\n\n## Speed\nSpeed is the distance traveled by an object per unit of time. It is calculated as:\n\\[ \\text{speed} = \\frac{\\text{distance traveled}}{\\text{time}} \\]\n\n## Velocity\nVelocity is speed in a given direction;... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 149,
"split": "train",
"text": "# Physics Concepts\n\n## Speed\nSpeed is the distance traveled by an object per unit of time. It is calculated as:\n\\[ \\text{speed} = \\frac{\\text{distance traveled}}{\\text{time}} \\]\n\n## Velocity\nVelocity is speed in a given direction;... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "float",
"index": 150,
"split": "train",
"text": "# Inter 1st Year Maths 1B: Direction Cosines and Direction Ratios\n\n## Overview\nThis document covers the fundamental formulas and theorems related to direction cosines and direction ratios in mathematics.\n\n### 1. Direction Cosines and Their ... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 150,
"split": "train",
"text": "# Inter 1st Year Maths 1B: Direction Cosines and Direction Ratios\n\n## Overview\nThis document covers the fundamental formulas and theorems related to direction cosines and direction ratios in mathematics.\n\n### 1. Direction Cosines and Thei... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 150,
"split": "train",
"text": "# Inter 1st Year Maths 1B: Direction Cosines and Direction Ratios\n\n## Overview\nThis document covers the fundamental formulas and theorems related to direction cosines and direction ratios in mathematics.\n\n### 1. Direction Cosines and Thei... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 151,
"split": "train",
"text": "# Math Help Forum\n\n## Determinant, Eigenvalue Discussion\n\n### Problem Statement\n\nHow do you find the left eigenvalue for a matrix \\( P \\) which is an \\( N \\times N \\) matrix where all its entries are \\( \\frac{1}{N} \\)? I know tha... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 151,
"split": "train",
"text": "# Math Help Forum\n\n## Determinant, Eigenvalue Discussion\n\n### Problem Statement\n\nHow do you find the left eigenvalue for a matrix \\( P \\) which is an \\( N \\times N \\) matrix where all its entries are \\( \\frac{1}{N} \\)? I know tha... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 151,
"split": "train",
"text": "# Math Help Forum\n\n## Determinant, Eigenvalue Discussion\n\n### Problem Statement\n\nHow do you find the left eigenvalue for a matrix \\( P \\) which is an \\( N \\times N \\) matrix where all its entries are \\( \\frac{1}{N} \\)? I know tha... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 152,
"split": "train",
"text": "Explain schedule, serializability and two-phase locking policy. Prove that two-phase locking approach guarantees serializability and always produces serializable schedule. To answer this question correctly first define what two-phase locki... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 152,
"split": "train",
"text": "Explain schedule, serializability and two-phase locking policy. Prove that two-phase locking approach guarantees serializability and always produces serializable schedule. To answer this question correctly first define what two-phase locki... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 152,
"split": "train",
"text": "Explain schedule, serializability and two-phase locking policy. Prove that two-phase locking approach guarantees serializability and always produces serializable schedule. To answer this question correctly first define what two-phase locki... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 153,
"split": "train",
"text": "# Logarithm Error and Propagation in Measurement\n\n## Understanding Logarithmic Errors\n\nIn mathematical computations, particularly those involving logarithms, errors can propagate through calculations in ways that may not be immediately obv... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 153,
"split": "train",
"text": "# Logarithm Error and Propagation in Measurement\n\n## Understanding Logarithmic Errors\n\nIn mathematical computations, particularly those involving logarithms, errors can propagate through calculations in ways that may not be immediately obv... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 153,
"split": "train",
"text": "# Logarithm Error and Propagation in Measurement\n\n## Understanding Logarithmic Errors\n\nIn mathematical computations, particularly those involving logarithms, errors can propagate through calculations in ways that may not be immediately obv... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 154,
"split": "train",
"text": "Take the 2-minute tour ×\n\nI'm close to releasing a rails app with the common networking features (messaging, wall, etc.). I want to use some kind of background processing (most likely Bj) for off-loading tasks from the request/response c... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 154,
"split": "train",
"text": "Take the 2-minute tour ×\n\nI'm close to releasing a rails app with the common networking features (messaging, wall, etc.). I want to use some kind of background processing (most likely Bj) for off-loading tasks from the request/response c... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 154,
"split": "train",
"text": "Take the 2-minute tour ×\n\nI'm close to releasing a rails app with the common networking features (messaging, wall, etc.). I want to use some kind of background processing (most likely Bj) for off-loading tasks from the request/response c... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 155,
"split": "train",
"text": "Subscribe to WIRED Magazine\nDanger Room\n\nArmy Turns to Lasers for Copter Defense\n\nSome jerk has fired a heat-seeking missile at your Black Hawk. You’ve got a few options. You can try to dodge the thing, but good luck with that. You ca... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 155,
"split": "train",
"text": "Subscribe to WIRED Magazine\nDanger Room\n\nArmy Turns to Lasers for Copter Defense\n\nSome jerk has fired a heat-seeking missile at your Black Hawk. You’ve got a few options. You can try to dodge the thing, but good luck with that. You ca... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 155,
"split": "train",
"text": "Subscribe to WIRED Magazine\nDanger Room\n\nArmy Turns to Lasers for Copter Defense\n\nSome jerk has fired a heat-seeking missile at your Black Hawk. You’ve got a few options. You can try to dodge the thing, but good luck with that. You ca... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 156,
"split": "train",
"text": "Marine Ecology\n\nSouth African fur seal\n\nOctober 9, 2011, 9:46 pm\nContent Cover Image\n\nSouth African fur seals on Geyser Rock, Dyer Island, South Africa. Source: Klaus Jost\n\nThe South African fur seal (also Also known as the Cape f... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 156,
"split": "train",
"text": "Marine Ecology\n\nSouth African fur seal\n\nOctober 9, 2011, 9:46 pm\nContent Cover Image\n\nSouth African fur seals on Geyser Rock, Dyer Island, South Africa. Source: Klaus Jost\n\nThe South African fur seal (also Also known as the Cape f... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 156,
"split": "train",
"text": "Marine Ecology\n\nSouth African fur seal\n\nOctober 9, 2011, 9:46 pm\nContent Cover Image\n\nSouth African fur seals on Geyser Rock, Dyer Island, South Africa. Source: Klaus Jost\n\nThe South African fur seal (also Also known as the Cape f... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "float",
"index": 157,
"split": "train",
"text": "# Find the value of $\\sqrt{3} \\cdot \\cot (20^{\\circ}) - 4 \\cdot \\cos (20^{\\circ})$\n\nHow to find the value of $$\\sqrt{3} \\cdot \\cot (20^{\\circ}) - 4 \\cdot \\cos (20^{\\circ})$$ manually?\n\n**Trigonometry**\n\n---\n\n**Solution 1:**... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 157,
"split": "train",
"text": "# Find the value of $\\sqrt{3} \\cdot \\cot (20^{\\circ}) - 4 \\cdot \\cos (20^{\\circ})$\n\nHow to find the value of $$\\sqrt{3} \\cdot \\cot (20^{\\circ}) - 4 \\cdot \\cos (20^{\\circ})$$ manually?\n\n**Trigonometry**\n\n---\n\n**Solution 1:... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 157,
"split": "train",
"text": "# Find the value of $\\sqrt{3} \\cdot \\cot (20^{\\circ}) - 4 \\cdot \\cos (20^{\\circ})$\n\nHow to find the value of $$\\sqrt{3} \\cdot \\cot (20^{\\circ}) - 4 \\cdot \\cos (20^{\\circ})$$ manually?\n\n**Trigonometry**\n\n---\n\n**Solution 1:... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "float",
"index": 158,
"split": "train",
"text": "# The smallest distance between two vectors\n\n## Problem Statement\n\nA radar station tracks a jet fighter flying with constant speed. The radar station is considered to be at the origin. The fighter's starting position is \\( \\mathbf{r}_0 = 2... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 158,
"split": "train",
"text": "# The smallest distance between two vectors\n\n## Problem Statement\n\nA radar station tracks a jet fighter flying with constant speed. The radar station is considered to be at the origin. The fighter's starting position is \\( \\mathbf{r}_0 =... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 158,
"split": "train",
"text": "# The smallest distance between two vectors\n\n## Problem Statement\n\nA radar station tracks a jet fighter flying with constant speed. The radar station is considered to be at the origin. The fighter's starting position is \\( \\mathbf{r}_0 =... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 159,
"split": "train",
"text": "# Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids\n\n## By John Playfair\n\n### Contents\n\n1. **Book I**\n - **Definition**: Parallel straight line... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 159,
"split": "train",
"text": "# Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids\n\n## By John Playfair\n\n### Contents\n\n1. **Book I**\n - **Definition**: Parallel straight line... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 159,
"split": "train",
"text": "# Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids\n\n## By John Playfair\n\n### Contents\n\n1. **Book I**\n - **Definition**: Parallel straight line... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 160,
"split": "train",
"text": "Email updates\n\n\n\nOpen Access Highly Accessed Research\n\nSequencing and analysis of an Irish human genome\n\nPin Tong1, James GD Prendergast2, Amanda J Lohan1, Susan M Farrington23, Simon Cronin4, Nial Friel5, Dan G Bradley6, Orla Hard... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 160,
"split": "train",
"text": "Email updates\n\n\n\nOpen Access Highly Accessed Research\n\nSequencing and analysis of an Irish human genome\n\nPin Tong1, James GD Prendergast2, Amanda J Lohan1, Susan M Farrington23, Simon Cronin4, Nial Friel5, Dan G Bradley6, Orla Hard... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 160,
"split": "train",
"text": "Email updates\n\n\n\nOpen Access Highly Accessed Research\n\nSequencing and analysis of an Irish human genome\n\nPin Tong1, James GD Prendergast2, Amanda J Lohan1, Susan M Farrington23, Simon Cronin4, Nial Friel5, Dan G Bradley6, Orla Hard... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 161,
"split": "train",
"text": "# Euler's Φ Function Proofs\n\n## Prove or Disprove\n\n### 1. With two exceptions, if \\(1 \\leq n < m\\) then \\(\\Phi(n) < \\Phi(m)\\)\n\n**Rules Used:**\n1. If \\(p\\) is prime, then \\(\\Phi(p) = p - 1\\).\n2. If \\(p\\) is prime, then for... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 161,
"split": "train",
"text": "# Euler's Φ Function Proofs\n\n## Prove or Disprove\n\n### 1. With two exceptions, if \\(1 \\leq n < m\\) then \\(\\Phi(n) < \\Phi(m)\\)\n\n**Rules Used:**\n1. If \\(p\\) is prime, then \\(\\Phi(p) = p - 1\\).\n2. If \\(p\\) is prime, then for... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "float",
"index": 161,
"split": "train",
"text": "# Euler's Φ Function Proofs\n\n## Prove or Disprove\n\n### 1. With two exceptions, if \\(1 \\leq n < m\\) then \\(\\Phi(n) < \\Phi(m)\\)\n\n**Rules Used:**\n1. If \\(p\\) is prime, then \\(\\Phi(p) = p - 1\\).\n2. If \\(p\\) is prime, then for a... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 162,
"split": "train",
"text": "Take the 2-minute tour ×\n\nMeanwhile reading some introductory notes about the projective special linear group $PSL(2,q)$ wherein $q$ is the cardinal number of the field; I saw:\n\n....in a finite field of order $q$, the number of element... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 162,
"split": "train",
"text": "Take the 2-minute tour ×\n\nMeanwhile reading some introductory notes about the projective special linear group $PSL(2,q)$ wherein $q$ is the cardinal number of the field; I saw:\n\n....in a finite field of order $q$, the number of element... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | general | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "categorical",
"index": 162,
"split": "train",
"text": "Take the 2-minute tour ×\n\nMeanwhile reading some introductory notes about the projective special linear group $PSL(2,q)$ wherein $q$ is the cardinal number of the field; I saw:\n\n....in a finite field of order $q$, the number of element... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 163,
"split": "train",
"text": "### John Wilmes\n\n**Assistant Professor of Mathematics**\n\n**Contact Information** \nEmail: wilmes@brandeis.edu \nPhone: 781-736-3077 \nOffice: Goldsmith Building, 313\n\n**Departments/Programs** \n- Mathematics \n- Volen National Cente... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "float",
"index": 163,
"split": "train",
"text": "### John Wilmes\n\n**Assistant Professor of Mathematics**\n\n**Contact Information** \nEmail: wilmes@brandeis.edu \nPhone: 781-736-3077 \nOffice: Goldsmith Building, 313\n\n**Departments/Programs** \n- Mathematics \n- Volen National Center ... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 163,
"split": "train",
"text": "### John Wilmes\n\n**Assistant Professor of Mathematics**\n\n**Contact Information** \nEmail: wilmes@brandeis.edu \nPhone: 781-736-3077 \nOffice: Goldsmith Building, 313\n\n**Departments/Programs** \n- Mathematics \n- Volen National Cente... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 164,
"split": "train",
"text": "# Problem 70: Totient permutation\n\nEuler's Totient function, $\\phi(n)$ (sometimes called the phi function), is used to determine the number of positive numbers less than or equal to $n$ which are relatively prime to $n$. For example, as 1, ... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "float",
"index": 164,
"split": "train",
"text": "# Problem 70: Totient permutation\n\nEuler's Totient function, $\\phi(n)$ (sometimes called the phi function), is used to determine the number of positive numbers less than or equal to $n$ which are relatively prime to $n$. For example, as 1, 2,... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "float",
"index": 164,
"split": "train",
"text": "# Problem 70: Totient permutation\n\nEuler's Totient function, $\\phi(n)$ (sometimes called the phi function), is used to determine the number of positive numbers less than or equal to $n$ which are relatively prime to $n$. For example, as 1, 2,... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 165,
"split": "train",
"text": "# How long does it take me to get to the town centre from the 120 km/h sign?\n\n**Post by Exponential on Thu Feb 18, 2010 4:41 am**\n\n1 km away from the town there's a 120 km/h sign, 1/2 km away there is a 60 km/h sign, 1/3 km away there is a... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 165,
"split": "train",
"text": "# How long does it take me to get to the town centre from the 120 km/h sign?\n\n**Post by Exponential on Thu Feb 18, 2010 4:41 am**\n\n1 km away from the town there's a 120 km/h sign, 1/2 km away there is a 60 km/h sign, 1/3 km away there is a... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 3,
"style": "rule"
} | {
"answer_type": "integer",
"index": 165,
"split": "train",
"text": "# How long does it take me to get to the town centre from the 120 km/h sign?\n\n**Post by Exponential on Thu Feb 18, 2010 4:41 am**\n\n1 km away from the town there's a 120 km/h sign, 1/2 km away there is a 60 km/h sign, 1/3 km away there is a... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 1,
"style": "rule"
} | {
"answer_type": "integer",
"index": 166,
"split": "train",
"text": "## Force and Torque on Current Loops\n\nPatrick Ford \n363 views \n5 \n7\n\nWhen you have current loops, an interesting phenomenon occurs: magnetic forces and torques. Consider a current-carrying wire placed in a magnetic field; it will exp... |
questioner_given_difficulty_id | [
{
"content": "Your task is to generate a single self-contained question and its correct answer inspired by the given document.\nThe question must strictly satisfy both the difficulty level and the answer_type constraints.\n\nYou must output exactly one JSON object as specified below. \nAll reasoning MUST be pl... | math | {
"ground_truth": 2,
"style": "rule"
} | {
"answer_type": "integer",
"index": 166,
"split": "train",
"text": "## Force and Torque on Current Loops\n\nPatrick Ford \n363 views \n5 \n7\n\nWhen you have current loops, an interesting phenomenon occurs: magnetic forces and torques. Consider a current-carrying wire placed in a magnetic field; it will exp... |
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