conversations listlengths 2 2 | question stringlengths 11 6.18k ⌀ | source stringclasses 8
values | id int64 19 50k ⌀ | prompt listlengths 2 2 | answer stringlengths 1 1.28k ⌀ | 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given that \\( a \\) and \\( b \\) are nonzero real constants, and the set \\( S=\\{x \\mid x=an+b, n \\in \\mathbf{N}^{-}\\} \\), find the necessary and sufficient condition for the existence of \\( x_0 \\), \\( q \\in \\mathbf{R} \\)... | Given that \( a \) and \( b \) are nonzero real constants, and the set \( S=\{x \mid x=an+b, n \in \mathbf{N}^{-}\} \), find the necessary and sufficient condition for the existence of \( x_0 \), \( q \in \mathbf{R} \), such that \( T=\{x \mid x=x_0 q^n, n \in \mathbf{N}^{*}\} \subset S \). | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | \frac{b}{a} \in \mathbb{Q} | original_rationalized | [
"To determine the necessary and sufficient condition for the existence of \\( x_0 \\) and \\( q \\in \\mathbf{R} \\) such that \\( T = \\{x \\mid x = x_0 q^n, n \\in \\mathbf{N}^*\\} \\subset S = \\{x \\mid x = an + b, n \\in \\mathbf{N}^- \\} \\), we need to analyze the structure of both sets.\n\nFirst, note that ... | [
false,
false
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"",
""
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[
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"from": "user",
"value": "The equation of the tangent line to the curve $y=x\\sin x$ at point $P(\\pi,0)$ is ( )\nA: $y=-\\pi x+\\pi^{2}$\nB: $y=\\pi x+\\pi^{2}$\nC: $y=-\\pi x-\\pi^{2}$\nD: $y=\\pi x-\\pi^{2}$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to find the equati... | The equation of the tangent line to the curve $y=x\sin x$ at point $P(\pi,0)$ is ( )
A: $y=-\pi x+\pi^{2}$
B: $y=\pi x+\pi^{2}$
C: $y=-\pi x-\pi^{2}$
D: $y=\pi x-\pi^{2}$ | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | A | original_rationalized | [
"To find the equation of the tangent line to the curve \\( y = x \\sin x \\) at the point \\( P(\\pi, 0) \\), we need to follow these steps:\n\n1. **Find the derivative of the function**:\n The given function is \\( y = x \\sin x \\). To find the slope of the tangent line at any point, we need the derivative \\( ... | [
false,
false
] | [
"",
""
] | {
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"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "4. The diagram shows a square $P Q R S$ with sides of length 2 . The point $T$ is the midpoint of $R S$, and $U$ lies on $Q R$ so that $\\angle S P T=\\angle T P U$.\nWhat is the length of $U R$ ?"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's try to figure... | 4. The diagram shows a square $P Q R S$ with sides of length 2 . The point $T$ is the midpoint of $R S$, and $U$ lies on $Q R$ so that $\angle S P T=\angle T P U$.
What is the length of $U R$ ? | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | \dfrac{1}{2} | original_rationalized | [
"Let's approach this problem methodically.\n\nFirstly, we have a square \\(PQRS\\) with each side equal to 2 units. Point \\(T\\) is the midpoint of \\(RS\\), meaning \\(RT = TS = 1\\) unit.\n\nSince \\(\\angle SPT = \\angle TPu\\), let's consider the properties of these angles. Because \\(P\\) is a vertex of the s... | [
false,
false
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"",
""
] | {
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"top_p": 0.8
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"model_name": "hosted_vll... | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
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[
{
"from": "user",
"value": "Return your final response within \\boxed{}. Define a sequence \\(\\left\\{x_{n}\\right\\}\\) with \\(x_{1}=1\\):\n\nFor \\(k>0\\),\n\\[ x_{2k}=\\begin{cases} \n2x_{k}, & \\text{if } k \\text{ is even}, \\\\\n2x_{k}+1, & \\text{if } k \\text{ is odd};\n\\end{cases} \\]\n\n\\[ x_{... | Define a sequence \(\left\{x_{n}\right\}\) with \(x_{1}=1\):
For \(k>0\),
\[ x_{2k}=\begin{cases}
2x_{k}, & \text{if } k \text{ is even}, \\
2x_{k}+1, & \text{if } k \text{ is odd};
\end{cases} \]
\[ x_{2k+1}=\begin{cases}
2x_{k}, & \text{if } k \text{ is odd}, \\
2x_{k}+1, & \text{if } k \text{ is even}.
\end{case... | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | \text{The sequence } \{x_n\} \text{ takes every positive integer exactly once.} | original_rationalized | [
"To prove that the sequence \\(\\left\\{x_{n}\\right\\}\\) can take every positive integer exactly once, we need to show two things:\n1. Every positive integer appears in the sequence.\n2. Each positive integer appears exactly once in the sequence.\n\nFirst, let's explore how the sequence is constructed. We start w... | [
false,
false
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"",
""
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"top_p": 0.8
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"model_name": "hosted_vll... | {
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"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
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[
{
"from": "user",
"value": "3. The length of the side of a regular hexagon $A_{1} A_{2} A_{3} A_{4} A_{5} A_{6}$ is $3 \\mathrm{~cm}$. Its (8) sides $\\overline{A_{1} A_{2}}, \\overline{A_{2} A_{3}}, \\overline{A_{3} A_{4}}, \\overline{A_{4} A_{5}}, \\overline{A_{5} A_{6}}, \\overline{A_{6} A_{1}}$ are exte... | 3. The length of the side of a regular hexagon $A_{1} A_{2} A_{3} A_{4} A_{5} A_{6}$ is $3 \mathrm{~cm}$. Its (8) sides $\overline{A_{1} A_{2}}, \overline{A_{2} A_{3}}, \overline{A_{3} A_{4}}, \overline{A_{4} A_{5}}, \overline{A_{5} A_{6}}, \overline{A_{6} A_{1}}$ are extended through the vertices $A_{2}, A_{3}, A_{4},... | null | null | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | 7 | original_rationalized | [
"To find the length of the side of the new hexagon formed by extending the sides of the original hexagon, let's analyze the geometric properties involved.\n\nGiven:\n- The side length of the original hexagon \\( A_1 A_2 = A_2 A_3 = \\cdots = A_6 A_1 = 3 \\text{ cm} \\).\n- Each side is extended by 5 cm beyond each ... | [
false,
false
] | [
"",
""
] | {
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"chat_template_applied": true,
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"n": 2,
"repetition_penalty": 1.1,
"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[
{
"from": "user",
"value": "Mr. Fat and Mr. Thin now have a new challenge. They need to eat 5 pounds of cereal together. If Mr. Fat still needs 20 minutes to eat a pound of cereal, but Mr. Thin's eating speed has increased to 25 minutes per pound, how long will it take them to finish the cereal?"
},
{
... | null | tiger_math | 16,687 | [
{
"content": "You like to solve problems by thinking step by step. Write out your reasoning then give your answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving an answer. You will never mention the hint at all, otherwise you will be penalyzed. For ex... | \dfrac{500}{9} | original_rationalized | [
"Let's start by calculating the rate at which each person eats cereal.\n\nFor Mr. Fat:\n- He eats 1 pound of cereal in 20 minutes.\n- Therefore, his rate is \\( \\frac{1 \\text{ pound}}{20 \\text{ minutes}} = \\frac{1}{20} \\text{ pounds per minute} \\).\n\nFor Mr. Thin:\n- He eats 1 pound of cereal in 25 minutes.\... | [
false,
false
] | [
"",
""
] | {
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"chat_template_applied": true,
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"temperature": 0.7,
"top_k": 20,
"top_p": 0.8
},
"model_name": "hosted_vll... | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[{"from":"user","value":"Driving under the influence of alcohol is a serious violation that endanger(...TRUNCATED) | "Driving under the influence of alcohol is a serious violation that endangers traffic safety. In ord(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | D | original_rationalized | ["To determine how long it takes for the driver's blood alcohol content to drop below the legal limi(...TRUNCATED) | [
false,
false
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"",
""
] | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
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"n_responses": 2
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[{"from":"user","value":"2. If $\\frac{x}{3 y}=\\frac{y}{2 x-5 y}=\\frac{6 x-15 y}{x}$, then the val(...TRUNCATED) | "2. If $\\frac{x}{3 y}=\\frac{y}{2 x-5 y}=\\frac{6 x-15 y}{x}$, then the value of $\\frac{4 x^{2}-5 (...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | A | original_rationalized | ["Let's start by analyzing the given equation:\n\n\\[\n\\frac{x}{3y} = \\frac{y}{2x - 5y} = \\frac{6(...TRUNCATED) | [
false,
false
] | [
"",
""
] | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[{"from":"user","value":"Return your final response within \\boxed{}. The first digit of a string of(...TRUNCATED) | "The first digit of a string of 2002 digits is a 1. Any two-digit number formed by consecutive digit(...TRUNCATED) | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | 8 | original_rationalized | ["Let's approach this problem methodically.\n\nFirstly, we need to identify all two-digit multiples (...TRUNCATED) | [
false,
false
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"",
""
] | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
[{"from":"user","value":"Find the slope of the line passing through $(4,2)$ and $(-1,-7)$."},{"from"(...TRUNCATED) | null | null | null | [{"content":"You like to solve problems by thinking step by step. Write out your reasoning then give(...TRUNCATED) | \dfrac{9}{5} | original_rationalized | ["To find the slope of a line passing through two points \\((x_1, y_1)\\) and \\((x_2, y_2)\\), we u(...TRUNCATED) | [
false,
false
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"",
""
] | {"api_url":"http://10.32.36.236:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
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