conversations listlengths 2 2 | question stringlengths 12 4.04k ⌀ | source stringclasses 8
values | id int64 21 50k ⌀ | prompt listlengths 2 2 | answer stringlengths 1 811 ⌀ | prompt_type stringclasses 1
value | model_responses__example_annotation listlengths 2 2 | model_responses__example_annotation__finish_reason_length_flags listlengths 2 2 | model_responses__example_annotation__length_partial_responses listlengths 2 2 | prompt__example_annotation__metadata dict | model_responses__example_annotation__metadata dict |
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"value": "Example 2.41. $I=\\int_{0}^{1} \\ln x d x$."
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"value": "<think>\nOkay, let me try to figure out how to solve the integral I = ∫ from 0 to 1 of ln(x) dx. Hmm, so the integral of the natural logarithm of x from 0 to 1. I remember that integratin... | Example 2.41. $I=\int_{0}^{1} \ln x d x$. | null | null | [
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"content": "You like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | -1 | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and going really deep into detail about how I should solve this integral \\( I = \\int_{0}^{1} \\ln x \\, dx \\).\n\n### Step-by-Step Plan\n\n1. **Understand the Integral:**\n - The integral involves the natural logarithm function, \\(\\ln x\... | [
false,
false
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"",
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[
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"value": "Example 8 (40th IMO National Team Selection Test) For non-negative real numbers $x_{1}, x_{2}, \\cdots, x_{n}$ satisfying the condition $\\sum_{i=1}^{n} x_{i}=1$, find the maximum value of $\\sum_{i=1}^{n}\\left(x_{j}^{4}-x_{j}^{5}\\right)$."
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... | Example 8 (40th IMO National Team Selection Test) For non-negative real numbers $x_{1}, x_{2}, \cdots, x_{n}$ satisfying the condition $\sum_{i=1}^{n} x_{i}=1$, find the maximum value of $\sum_{i=1}^{n}\left(x_{j}^{4}-x_{j}^{5}\right)$. | null | null | [
{
"content": "You like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | \dfrac{1}{12} | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Understanding the Problem\n\nWe are given \\( n \\) non-negative real numbers \\( x_1, x_2, \\ldots, x_n \\) such that their sum equals 1:\n\\[ \\sum_{i=1}^n x_i = 1. \\]\n\nW... | [
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[
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"value": "## 157. Math Puzzle $6 / 78$\n\nAt a class party, in addition to the milkshake drinks, various soda bottles were also emptied. There were more than 20 and fewer than 25, and specifically five times as many Astoria bottles as Cola, half as many Lemonade bottles as Astoria, and thr... | ## 157. Math Puzzle $6 / 78$
At a class party, in addition to the milkshake drinks, various soda bottles were also emptied. There were more than 20 and fewer than 25, and specifically five times as many Astoria bottles as Cola, half as many Lemonade bottles as Astoria, and three fewer Selters bottles than Astoria. How... | null | null | [
{
"content": "You like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | 24 | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Plan:\n\n1. **Identify Variables:**\n - Let \\( A \\) be the number of Astoria bottles.\n - Let \\( C \\) be the number of Cola bottles.\n - Let \\( L \\) be the number ... | [
false,
false
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"",
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[
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"value": "Return your final response within \\boxed{}. Let $S$ be the set of points on the rays forming the sides of a $120^{\\circ}$ angle, and let $P$ be a fixed point inside the angle on the angle bisector. Consider all distinct equilateral triangles $PQR$ with $Q$ and $R$ i... | Let $S$ be the set of points on the rays forming the sides of a $120^{\circ}$ angle, and let $P$ be a fixed point inside the angle on the angle bisector. Consider all distinct equilateral triangles $PQR$ with $Q$ and $R$ in $S$ . (Points $Q$ and $R$ may be on the same ray, and switching the names of $... | null | null | [
{
"content": "You like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | B | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Step-by-Step Plan:\n\n1. **Understand the Geometry**:\n - We have a \\(120^\\circ\\) angle.\n - The vertex of the angle is at the origin \\(O = (0, 0)\\).\n - One side o... | [
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"value": "2. Find the minimum value of the expression for $a, b>0$\n\n$$\n\\frac{(2 a+2 a b-b(b+1))^{2}+\\left(b-4 a^{2}+2 a(b+1)\\right)^{2}}{4 a^{2}+b^{2}}\n$$"
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"value": "<think>\nOkay, so I need to find the minimum value of this expression:\n\n$$\n\... | 2. Find the minimum value of the expression for $a, b>0$
$$
\frac{(2 a+2 a b-b(b+1))^{2}+\left(b-4 a^{2}+2 a(b+1)\right)^{2}}{4 a^{2}+b^{2}}
$$ | null | null | [
{
"content": "You like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | 1 | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\n### Plan:\n\n1. **Simplify the Expression:**\n - Start by simplifying the numerator of the given expression:\n \\[\n \\frac{(2a + 2ab - b(b+1))^2 + (b - 4a^2 + 2a(b+1))^... | [
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"",
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[
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"value": "Convert the base-7 number $305_{(7)}$ to a base-5 number."
},
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"value": "<think>\nAlright, so I need to convert the base-7 number 305_{(7)} to a base-5 number. Hmm, okay. Let's think about how to approach this. I remember that when converting num... | Convert the base-7 number $305_{(7)}$ to a base-5 number. | null | null | [
{
"content": "You like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | 1102_{(5)} | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and going really deep into detail about how I should solve this.\n\n1. **Understand the Problem:**\n - We need to convert a base-7 number \\(305_{(7)}\\) to a base-5 number.\n \n2. **Convert from Base-7 to Base-10:**\n - The first step in... | [
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"value": "Brandon has a collection of 20 baseball cards. Malcom has 8 more cards than Brandon. However, then Malcom gives x% of his cards to his friend Mark. How many cards does Malcom have left?\nIf we know the answer to the above question is 14, what is the value of unknown variable x... | null | null | null | [
{
"content": "You like to solve problems by understanding the problem, writing a plan, executing the plan, then giving an answer. Write a plan that when reasoned over would solve the question then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end witho... | 50 | plan_and_execute | [
"First, I'll try to understand the problem better by writing out a plan and go really deep into detail about how I should solve this.\n\nStep 1: Determine the initial number of cards Malcolm has.\n- Brandon has 20 cards.\n- Malcolm has 8 more cards than Brandon, so Malcolm initially has \\(20 + 8 = 28\\) cards.\n\n... | [
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false
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[{"from":"user","value":"Given that the line $ax + by - 3 = 0$ has no common points with the circle (...TRUNCATED) | "Given that the line $ax + by - 3 = 0$ has no common points with the circle $x^2 + y^2 = 3$, let the(...TRUNCATED) | null | null | [{"content":"You like to solve problems by understanding the problem, writing a plan, executing the (...TRUNCATED) | C | plan_and_execute | ["First, I'll try to understand the problem better by writing out a plan and go really deep into det(...TRUNCATED) | [
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[{"from":"user","value":"Given the vectors $\\overrightarrow{a}=(1,2)$ and $2\\overrightarrow{a}+ \\(...TRUNCATED) | "Given the vectors $\\overrightarrow{a}=(1,2)$ and $2\\overrightarrow{a}+ \\overrightarrow{b}=(3,2)$(...TRUNCATED) | null | null | [{"content":"You like to solve problems by understanding the problem, writing a plan, executing the (...TRUNCATED) | B | plan_and_execute | ["First, I'll try to understand the problem better by writing out a plan and go really deep into det(...TRUNCATED) | [
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[{"from":"user","value":"Prove that $1 + \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\ldots + \\fr(...TRUNCATED) | "Prove that $1 + \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\ldots + \\frac{1}{2^{n}-1} > \\frac{(...TRUNCATED) | null | null | [{"content":"You like to solve problems by understanding the problem, writing a plan, executing the (...TRUNCATED) | 2^k | plan_and_execute | ["First, I'll try to understand the problem better by writing out a plan and go really deep into det(...TRUNCATED) | [
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