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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | \frac{b}{a} \in \mathbb{Q} | rephrase_rationalized | [
"Rewritten Question: Given \\( 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 \\) and \\( q \\in \\mathbf{R} \\) such that \\( T = \\{x \\mid x = x_0 q^n, n \\in \\math... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"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": "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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | A | rephrase_rationalized | [
"Rewritten Question: Find the equation of the tangent line to the curve \\( y = x \\sin x \\) at the point \\( P(\\pi, 0) \\).\n\nStep 1: Calculate the derivative of \\( y = x \\sin x \\).\n\\[ y' = \\frac{d}{dx}(x \\sin x) = x \\cos x + \\sin x \\]\n\nStep 2: Evaluate the derivative at \\( x = \\pi \\).\n\\[ y'(\\... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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": "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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | \dfrac{1}{2} | rephrase_rationalized | [
"Rewritten Question: A square \\( PQRS \\) has side lengths of 2. Point \\( T \\) is the midpoint of \\( RS \\), and \\( U \\) lies on \\( QR \\) such that \\( \\angle SP T = \\angle TP U \\). Find the length of \\( UR \\).\n\nStep 1: Identify coordinates for points.\n- Let \\( P = (0, 2) \\), \\( Q = (2, 2) \\), \... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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": "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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | \text{The sequence } \{x_n\} \text{ takes every positive integer exactly once.} | rephrase_rationalized | [
"Rewritten Question: Define a sequence \\(\\left\\{x_{n}\\right\\}\\) with \\(x_{1}=1\\). For \\(k>0\\),\n\n- If \\(k\\) is even, then \\(x_{2k} = 2x_k\\).\n- If \\(k\\) is odd, then \\(x_{2k} = 2x_k + 1\\).\n\n- If \\(k\\) is even, then \\(x_{2k+1} = 2x_k\\).\n- If \\(k\\) is odd, then \\(x_{2k+1} = 2x_k + 1\\).\n... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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": "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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | 7 | rephrase_rationalized | [
"Rewritten Question: \nThe length of each side of a regular hexagon is 3 cm. Each side is extended by 5 cm beyond one vertex to form another regular hexagon. What is the length of each side of the new hexagon?\n\nStep 1: Visualize the problem.\n- We have a regular hexagon \\(A_1A_2A_3A_4A_5A_6\\) with each side bei... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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 answer questions by saying \"Rewritten Question: \" then rewriting the question to only contain what is needed to solve it and then think step by step and then you give your final answer in \"<answer>\n(your answer)\n</answer>\". You always end with </answer>, you never ever end without giving... | \dfrac{500}{9} | rephrase_rationalized | [
"Rewritten Question: \nIf Mr. Fat takes 20 minutes per pound and Mr. Thin takes 25 minutes per pound to eat cereal, how long will it take for both to finish 5 pounds of cereal together?\n\nStep 1: Calculate the rate at which each person eats.\n- Mr. Fat's rate: \\( \\frac{1 \\text{ pound}}{20 \\text{ minutes}} \\)\... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.236:9080/v1",
"backend": "litellm",
"chat_template_applied": true,
"generation_params": {
"chat_template_applied": true,
"max_tokens": 4096,
"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":"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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | D | rephrase_rationalized | ["Rewritten Question: A driver has an alcohol content of $1mg/mL$ in their blood. The alcohol conten(...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":"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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | A | rephrase_rationalized | ["Rewritten Question: If \\(\\frac{x}{3y} = \\frac{y}{2x - 5y} = \\frac{6x - 15y}{x}\\), find the va(...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 answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | 8 | rephrase_rationalized | ["Rewritten Question: A string of 2002 digits starts with 1. Every two-digit number formed by consec(...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":"Find the slope of the line passing through $(4,2)$ and $(-1,-7)$."},{"from"(...TRUNCATED) | null | null | null | [{"content":"You answer questions by saying \"Rewritten Question: \" then rewriting the question to (...TRUNCATED) | \dfrac{9}{5} | rephrase_rationalized | ["Rewritten Question: Find the slope of the line passing through (4, 2) and (-1, -7).\n\nTo find the(...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
} |
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