conversations listlengths 2 2 | question stringlengths 13 7.47k ⌀ | source stringclasses 8
values | id int64 1 50k ⌀ | prompt listlengths 2 2 | answer stringlengths 1 508 ⌀ | prompt_type stringclasses 2
values | 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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[
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"value": "Given a line $l:x-my+\\sqrt{3}m=0$ has a point $M$ on it that satisfies the product of the slopes of the lines connecting $M$ to points $A(-1,0)$ and $B(1,0)$, denoted as $k_{MA}$ and $k_{MB}$, is $3$, then the range of the real number $m$ is $(\\quad)$\n\nA: $[-\\sqrt{6},\\sqrt{... | Given a line $l:x-my+\sqrt{3}m=0$ has a point $M$ on it that satisfies the product of the slopes of the lines connecting $M$ to points $A(-1,0)$ and $B(1,0)$, denoted as $k_{MA}$ and $k_{MB}$, is $3$, then the range of the real number $m$ is $(\quad)$
A: $[-\sqrt{6},\sqrt{6}]$
B: $\left( -\infty,-\frac{\sqrt{6}}{6} \... | 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... | C | plan_and_execute_rationalized | [
"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 1: Understand the Line Equation and Point M\nThe given line equation is \\( l: x - my + \\sqrt{3}m = 0 \\). We need to find a point \\( M(x_0, y_0) \\) on this line such ... | [
false,
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"",
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"chat_template_applied": true,
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"n": 2,
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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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[
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"value": "Given that $i$ is the imaginary unit, the complex number $z=(-1-2i)i$ corresponds to a point in the complex plane located in $\\text{( }\\,\\,\\text{ )}$.\nA: the first quadrant\nB: the second quadrant\nC: the third quadrant\nD: the fourth quadrant"
},
{
"from": "assistan... | Given that $i$ is the imaginary unit, the complex number $z=(-1-2i)i$ corresponds to a point in the complex plane located in $\text{( }\,\,\text{ )}$.
A: the first quadrant
B: the second quadrant
C: the third quadrant
D: the fourth quadrant | 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... | D | plan_and_execute_rationalized | [
"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:\n1. **Understand the Problem**: We need to determine the location of the point corresponding to the complex number \\( z = (-1 - 2i)i \\) in the complex pla... | [
false,
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"",
""
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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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[
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"value": "Return your final response within \\boxed{}. There are more than 3 but fewer than 15 children in class 7B. For New Year, Santa Claus came to them with a sack containing 195 candies. After distributing candies equally to all the children in the class, Santa discovered that there w... | There are more than 3 but fewer than 15 children in class 7B. For New Year, Santa Claus came to them with a sack containing 195 candies. After distributing candies equally to all the children in the class, Santa discovered that there were 8 candies left in the sack. How many candies did each child receive? | 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... | 17 | plan_and_execute_rationalized | [
"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\nThe total number of candies is 195, and after distributing them equally among the children, 8 candies remain. This means if we subtract the remaining candies from the total, we ge... | [
false,
false
] | [
"",
""
] | {
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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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[
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"value": "In the acute dihedral angle $\\alpha-l-\\beta$, line $a$ is contained in plane $\\alpha$, line $b$ is contained in plane $\\beta$, and both $a$ and $b$ intersect line $l$ obliquely, then ( )\nA: $a$ may be perpendicular to $b$, and may also be parallel to $b$\nB: $a$ may be perpe... | In the acute dihedral angle $\alpha-l-\beta$, line $a$ is contained in plane $\alpha$, line $b$ is contained in plane $\beta$, and both $a$ and $b$ intersect line $l$ obliquely, then ( )
A: $a$ may be perpendicular to $b$, and may also be parallel to $b$
B: $a$ may be perpendicular to $b$, but cannot be parallel to $b$... | 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_rationalized | [
"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\n1. **Understand the Geometry**: The problem describes two planes \\(\\alpha\\) and \\(\\beta\\) forming an acute dihedral angle \\(l\\). Line \\(a\\) lies within \\(\\alpha\\) and... | [
false,
false
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"",
""
] | {
"api_url": "http://10.32.36.232:9080/v1",
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"chat_template_applied": true,
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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": "Calculate: $|-\\dfrac{1}{2}|+\\left(-1\\right)^{2019}+2^{-1}-\\left(2-\\sqrt{2}\\right)^{0}+2\\cos 45^{\\circ}$."
},
{
"from": "assistant",
"value": "<think>\nOkay, let me try to solve this problem step by step. The problem is: Calculate |−1/2| + (−1)^2019 + 2^−1 − (2... | Calculate: $|-\dfrac{1}{2}|+\left(-1\right)^{2019}+2^{-1}-\left(2-\sqrt{2}\right)^{0}+2\cos 45^{\circ}$. | 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... | \sqrt{2} - 1 | plan_and_execute_rationalized | [
"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\n1. **Evaluate the Absolute Value**: The term \\( |-\\frac{1}{2}| \\) means we need to find the absolute value of \\(-\\frac{1}{2}\\). Since the absolute value of any negative numb... | [
false,
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] | [
"",
""
] | {
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"backend": "litellm",
"chat_template_applied": true,
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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
} |
[
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"value": "13. $A B C D$ is a convex quadrilateral in which $A C$ and $B D$ meet at $P$. Given $P A=1$, $P B=2, P C=6$ and $P D=3$. Let $O$ be the circumcentre of $\\triangle P B C$. If $O A$ is perpendicular to $A D$, find the circumradius of $\\triangle P B C$.\n(2 marks)\n$A B C D$ is a ... | 13. $A B C D$ is a convex quadrilateral in which $A C$ and $B D$ meet at $P$. Given $P A=1$, $P B=2, P C=6$ and $P D=3$. Let $O$ be the circumcentre of $\triangle P B C$. If $O A$ is perpendicular to $A D$, find the circumradius of $\triangle P B C$.
(2 marks)
$A B C D$ is a convex quadrilateral, in which $A C$ and $B ... | 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... | 3 | plan_and_execute_rationalized | [
"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 convex quadrilateral \\(ABCD\\) with diagonals \\(AC\\) and \\(BD\\) intersecting at point \\(P\\).\n - ... | [
false,
false
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"",
""
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"chat_template_applied": true,
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"chat_template_applied": true,
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"n": 2,
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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
} |
[
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"value": "Maria is preparing a salad. She uses 20 cherry tomatoes, three times as many cucumber slices, and 8 more carrot sticks than cherry tomatoes. If the salad is divided into 4 portions, and all ingredients are distributed evenly, how many pieces of vegetables altogether are in each p... | null | nvidia_math | 20,530 | [
{
"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... | 27 | plan_and_execute_rationalized | [
"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\n1. Identify the quantities of each ingredient:\n - Maria uses 20 cherry tomatoes.\n - The number of cucumber slices is three times the number of cherry tomatoes, so \\(3 \\tim... | [
false,
false
] | [
"",
""
] | {
"api_url": "http://10.32.36.232:9080/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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[
{
"from": "user",
"value": "If $\\log_{2}a + \\log_{ \\frac {1}{2}}b = 2$, then ( )\n\nA: $a=2b$\nB: $b=2a$\nC: $a=4b$\nD: $b=4a$"
},
{
"from": "assistant",
"value": "<think>\nOkay, so I need to solve this logarithm problem. Let me see... The equation given is log base 2 of a plus log base 1/2 o... | If $\log_{2}a + \log_{ \frac {1}{2}}b = 2$, then ( )
A: $a=2b$
B: $b=2a$
C: $a=4b$
D: $b=4a$ | 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... | C | plan_and_execute_rationalized | [
"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 given equation**: The equation we have is:\n \\[\n \\log_{2}a + \\log_{\\frac{1}{2}}b = 2\n \\]\n\n2. **Simplify the logarithmi... | [
false,
false
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"",
""
] | {
"api_url": "http://10.32.36.232:9080/v1",
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"chat_template_applied": true,
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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
} |
[
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"value": "11. (2002 National Competition Question) Real numbers $a, b, c$ and a positive number $\\lambda$ make $f(x)=x^{3}+a x^{2}+b x+c$ have three real roots $x_{1}, x_{2}, x_{3}$, and satisfy\n(1) $x_{2}-x_{1}=\\lambda$; (2) $x_{3}>\\frac{1}{2}\\left(x_{1}+x_{2}\\right)$.\nFind the max... | 11. (2002 National Competition Question) Real numbers $a, b, c$ and a positive number $\lambda$ make $f(x)=x^{3}+a x^{2}+b x+c$ have three real roots $x_{1}, x_{2}, x_{3}$, and satisfy
(1) $x_{2}-x_{1}=\lambda$; (2) $x_{3}>\frac{1}{2}\left(x_{1}+x_{2}\right)$.
Find the maximum value of $\frac{2 a^{3}+27 c-9 a b}{\lambd... | 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{3\sqrt{3}}{2} | plan_and_execute_rationalized | [
"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 1: Understand the Roots and Given Conditions\n\nGiven \\( f(x) = x^3 + ax^2 + bx + c \\) has roots \\( x_1, x_2, x_3 \\). We are given:\n1. \\( x_2 - x_1 = \\lambda \\)\n... | [
false,
false
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"",
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"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{}. How many even integers are the(...TRUNCATED) | "How many even integers are there between $200$ and $700$ whose digits are all different and come fr(...TRUNCATED) | null | null | [{"content":"You like to solve problems by understanding the problem, writing a plan, executing the (...TRUNCATED) | B | plan_and_execute_rationalized | ["First, I'll try to understand the problem better by writing out a plan and go really deep into det(...TRUNCATED) | [
false,
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"",
""
] | {"api_url":"http://10.32.36.232:9080/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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