conversations listlengths 2 2 | question stringlengths 12 5.4k ⌀ | source stringclasses 8
values | id int64 21 50k ⌀ | prompt listlengths 2 2 | answer stringlengths 1 560 ⌀ | 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": "Given the line $ax+y+1=0$ always passes through a fixed point, the coordinates of this fixed point are \\_\\_\\_\\_\\_\\_."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem says that the line ax + y + 1 = 0 always passes through a fixed point,... | Given the line $ax+y+1=0$ always passes through a fixed point, the coordinates of this fixed point are \_\_\_\_\_\_. | 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... | (0, -1) | rephrase_rationalized | [
"Rewritten Question: Given the line \\( ax + y + 1 = 0 \\) always passes through a fixed point, find the coordinates of this fixed point.\n\nTo determine the fixed point through which the line \\( ax + y + 1 = 0 \\) always passes, we need to identify a point \\((x_0, y_0)\\) such that substituting these values into... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/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": "Given $x\\_1=\\log \\_{\\frac {1}{3}}2$, $x\\_2=2^{-\\frac {1}{2}}$, and $(\\frac {1}{3})^{x3}=\\log \\_{3}x\\_{3}$, determine the correct relationship among $x\\_1$, $x\\_2$, and $x\\_3$.\n\nA: $x\\_1 < x\\_3 < x\\_2$\nB: $x\\_2 < x\\_1 < x\\_3$\nC: $x\\_1 < x\\_2 < x\\_3$\nD: $... | Given $x\_1=\log \_{\frac {1}{3}}2$, $x\_2=2^{-\frac {1}{2}}$, and $(\frac {1}{3})^{x3}=\log \_{3}x\_{3}$, determine the correct relationship among $x\_1$, $x\_2$, and $x\_3$.
A: $x\_1 < x\_3 < x\_2$
B: $x\_2 < x\_1 < x\_3$
C: $x\_1 < x\_2 < x\_3$
D: $x\_3 < x\_1 < x\_2$ | 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... | C | rephrase_rationalized | [
"Rewritten Question: Given \\(x_1 = \\log_{\\frac{1}{3}} 2\\), \\(x_2 = 2^{-\\frac{1}{2}}\\), and \\(\\left(\\frac{1}{3}\\right)^{x_3} = \\log_3 x_3\\), determine the correct order of \\(x_1\\), \\(x_2\\), and \\(x_3\\).\n\nStep 1: Evaluate \\(x_1 = \\log_{\\frac{1}{3}} 2\\).\nSince the base \\(\\frac{1}{3}\\) is l... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/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": "1. Given sets\n$$\n\\begin{array}{l}\nS_{1}=\\left\\{(x, y) \\mid \\lg \\left(1+x^{2}+y^{2}\\right) \\leqslant 1+\\lg (x+y)\\right\\}, \\\\\nS_{2}=\\left\\{(x, y) \\mid \\lg \\left(2+x^{2}+y^{2}\\right) \\leqslant 2+\\lg (x+y)\\right\\} .\n\\end{array}\n$$\n\nThen the ratio of th... | 1. Given sets
$$
\begin{array}{l}
S_{1}=\left\{(x, y) \mid \lg \left(1+x^{2}+y^{2}\right) \leqslant 1+\lg (x+y)\right\}, \\
S_{2}=\left\{(x, y) \mid \lg \left(2+x^{2}+y^{2}\right) \leqslant 2+\lg (x+y)\right\} .
\end{array}
$$
Then the ratio of the area of $S_{2}$ to the area of $S_{1}$ is ( ).
(A) 99
(B) 100
(C) 101
... | 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... | D | rephrase_rationalized | [
"Rewritten Question: \nGiven sets\n$$\n\\begin{array}{l}\nS_{1}=\\left\\{(x, y) \\mid \\lg \\left(1+x^{2}+y^{2}\\right) \\leqslant 1+\\lg (x+y)\\right\\}, \\\\\nS_{2}=\\left\\{(x, y) \\mid \\lg \\left(2+x^{2}+y^{2}\\right) \\leqslant 2+\\lg (x+y)\\right\\}.\n\\end{array}\n$$\nFind the ratio of the area of \\( S_{2}... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/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": "Given that function $f(x)$ is an even function defined on $\\mathbb{R}$ and is monotonically increasing in the interval $[0,+\\infty)$. If the real number $a$ satisfies $f(\\log_{2}a)+f(\\log_{\\frac{1}{2}}a) < 2f(1)$, determine the range of $a$.\n\nA: $[1,2]$\nB: $(0, \\frac{1}{... | Given that function $f(x)$ is an even function defined on $\mathbb{R}$ and is monotonically increasing in the interval $[0,+\infty)$. If the real number $a$ satisfies $f(\log_{2}a)+f(\log_{\frac{1}{2}}a) < 2f(1)$, determine the range of $a$.
A: $[1,2]$
B: $(0, \frac{1}{2}]$
C: $(\frac{1}{2},2)$
D: $(0,2]$ | 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... | C | rephrase_rationalized | [
"Rewritten Question: Given that function \\( f(x) \\) is an even function defined on \\( \\mathbb{R} \\) and is monotonically increasing in the interval \\( [0, +\\infty) \\). If the real number \\( a \\) satisfies \\( f(\\log_{2}a) + f(\\log_{\\frac{1}{2}}a) < 2f(1) \\), determine the range of \\( a \\).\n\nStep 1... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/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": "The organizing committee of the sports meeting needs to select four volunteers from Xiao Zhang, Xiao Zhao, Xiao Li, Xiao Luo, and Xiao Wang to take on four different tasks: translation, tour guide, etiquette, and driver. If Xiao Zhang and Xiao Zhao can only take on the first two ... | The organizing committee of the sports meeting needs to select four volunteers from Xiao Zhang, Xiao Zhao, Xiao Li, Xiao Luo, and Xiao Wang to take on four different tasks: translation, tour guide, etiquette, and driver. If Xiao Zhang and Xiao Zhao can only take on the first two tasks, while the other three can take on... | 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... | 36 | rephrase_rationalized | [
"Rewritten Question: \nXiao Zhang and Xiao Zhao can only take on the translation or tour guide task. The other three volunteers (Xiao Li, Xiao Luo, and Xiao Wang) can take on any of the four tasks. How many different dispatch plans are there?\n\nStep 1: Determine how many ways we can assign tasks to Xiao Zhang and ... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/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": "Given that point $Q(a-1,a+2)$ lies on the $x$-axis, what are the coordinates of point $Q$?\n\nA: $(-3,0)$\n\nB: $(3,0)$\n\nC: $(0,3)$\n\nD: $(0,-3)$"
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem is about finding the coordinates of point Q,... | Given that point $Q(a-1,a+2)$ lies on the $x$-axis, what are the coordinates of point $Q$?
A: $(-3,0)$
B: $(3,0)$
C: $(0,3)$
D: $(0,-3)$ | 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: Given that point \\( Q(a-1, a+2) \\) lies on the x-axis, find the coordinates of point \\( Q \\).\n\nTo determine the coordinates of point \\( Q \\), we need to use the fact that any point lying on the x-axis has its y-coordinate equal to 0. Therefore, for point \\( Q(a-1, a+2) \\):\n\n1. The y... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/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": "## Task B-2.3.\n\nCalculate:\n\n$$\n\\frac{\\left(1+\\frac{1}{3}\\right)\\left(1+\\frac{1}{5}\\right) \\cdot \\ldots \\cdot\\left(1+\\frac{1}{2 n+1}\\right) \\cdot \\ldots \\cdot\\left(1+\\frac{1}{4047}\\right)}{\\sqrt{\\left(1-\\frac{1}{3^{2}}\\right)\\left(1-\\frac{1}{5^{2}}\\r... | ## Task B-2.3.
Calculate:
$$
\frac{\left(1+\frac{1}{3}\right)\left(1+\frac{1}{5}\right) \cdot \ldots \cdot\left(1+\frac{1}{2 n+1}\right) \cdot \ldots \cdot\left(1+\frac{1}{4047}\right)}{\sqrt{\left(1-\frac{1}{3^{2}}\right)\left(1-\frac{1}{5^{2}}\right) \cdot \ldots \cdot\left(1-\frac{1}{(2 n+1)^{2}}\right) \cdot \ldo... | 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... | \sqrt{2024} | rephrase_rationalized | [
"Rewritten Question: \n\nCalculate:\n\n$$\n\\frac{\\left(1+\\frac{1}{3}\\right)\\left(1+\\frac{1}{5}\\right) \\cdots \\left(1+\\frac{1}{4047}\\right)}{\\sqrt{\\left(1-\\frac{1}{9}\\right)\\left(1-\\frac{1}{25}\\right) \\cdots \\left(1-\\frac{1}{4047^2}\\right)}}\n$$\n\nStep 1: Simplify the numerator.\nEach term in ... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/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": "Solve the following system of equations:\n\n$$\n\\begin{gathered}\n\\frac{10}{2 x+3 y-29}+\\frac{9}{7 x-8 y+24}=8 \\\\\n\\frac{2 x+3 y-29}{2}=\\frac{7 x-8 y}{3}+8\n\\end{gathered}\n$$"
},
{
"from": "assistant",
"value": "<think>\nAlright, so I need to solve this syste... | Solve the following system of equations:
$$
\begin{gathered}
\frac{10}{2 x+3 y-29}+\frac{9}{7 x-8 y+24}=8 \\
\frac{2 x+3 y-29}{2}=\frac{7 x-8 y}{3}+8
\end{gathered}
$$ | 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... | (5, 7) | rephrase_rationalized | [
"Rewritten Question: Solve the following system of equations:\n\\[\n\\begin{cases}\n\\frac{10}{2x + 3y - 29} + \\frac{9}{7x - 8y + 24} = 8 \\\\\n\\frac{2x + 3y - 29}{2} = \\frac{7x - 8y}{3} + 8\n\\end{cases}\n\\]\n\nStep 1: Simplify the second equation.\nLet \\( a = 2x + 3y - 29 \\) and \\( b = 7x - 8y + 24 \\).\nT... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/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": "the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 80 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ? Please respond by ... | null | 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... | 159.2\% | rephrase_rationalized | [
"Rewritten Question: \nThe length of each side of square a is doubled to make square b. Then, the length of the side of square b is increased by 80% to make square c. By what percent is the area of square c greater than the sum of the areas of squares a and b?\n\nLet's denote:\n- The side length of square a as \\( ... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/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": "Given the function $f(2^x)$ has a domain of $[1, 2]$, find the domain of $f(\\log_2 x)$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let's see. The problem says that the function f(2^x) has a domain of [1, 2], and we need to find the domain of f(log₂ x). Hmm, ... | Given the function $f(2^x)$ has a domain of $[1, 2]$, find the domain of $f(\log_2 x)$. | 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... | [4, 16] | rephrase_rationalized | [
"Rewritten Question: Given the function \\( f(2^x) \\) has a domain of \\([1, 2]\\), find the domain of \\( f(\\log_2 x) \\).\n\nStep 1: Understand the given domain for \\( f(2^x) \\).\n- The domain of \\( f(2^x) \\) is \\([1, 2]\\). This means \\( x \\) ranges from 1 to 2.\n- When \\( x = 1 \\), \\( 2^x = 2^1 = 2 ... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/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": "Given that the functions $f(x)$ and $g(x)$ defined on $\\mathbb{R}$ satisfy $\\frac{f(x)}{g(x)} = b^x$, and $f'(x)g(x) < f(x)g'(x)$, $\\frac{f(1)}{g(1)} + \\frac{f(-1)}{g(-1)} = \\frac{5}{2}$. If $\\{a_n\\}$ is a positive geometric sequence and $a_5a_7 + 2a_6a_8 + a_4a_{12} = \\f... | Given that the functions $f(x)$ and $g(x)$ defined on $\mathbb{R}$ satisfy $\frac{f(x)}{g(x)} = b^x$, and $f'(x)g(x) < f(x)g'(x)$, $\frac{f(1)}{g(1)} + \frac{f(-1)}{g(-1)} = \frac{5}{2}$. If $\{a_n\}$ is a positive geometric sequence and $a_5a_7 + 2a_6a_8 + a_4a_{12} = \frac{f(4)}{g(4)}$, find the value of $a_6 + a_8$. | 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}{4} | rephrase_rationalized | [
"Rewritten Question: Given \\( \\frac{f(x)}{g(x)} = b^x \\), \\( f'(x)g(x) < f(x)g'(x) \\), and \\( \\frac{f(1)}{g(1)} + \\frac{f(-1)}{g(-1)} = \\frac{5}{2} \\). Let \\( \\{a_n\\} \\) be a positive geometric sequence such that \\( a_5a_7 + 2a_6a_8 + a_4a_{12} = \\frac{f(4)}{g(4)} \\). Find \\( a_6 + a_8 \\).\n\nSte... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.231:9080/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
} |
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