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 |
|---|---|---|---|---|---|---|---|---|---|---|---|
[
{
"from": "user",
"value": "Example 2.41. $I=\\int_{0}^{1} \\ln x d x$."
},
{
"from": "assistant",
"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 | [
{
"content": "You like to find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | -1 | alternative | [
"To solve the integral \\( I = \\int_{0}^{1} \\ln x \\, dx \\), let's explore different methods:\n\n**Method 1: Integration by Parts**\nWe can use integration by parts where we set:\n\\[ u = \\ln x \\quad \\text{and} \\quad dv = dx \\]\nThen,\n\\[ du = \\frac{1}{x} \\, dx \\quad \\text{and} \\quad v = x \\]\n\nUsin... | [
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": "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 $\\sum_{i=1}^{n}\\left(x_{j}^{4}-x_{j}^{5}\\right)$."
},
{
"from": "assistant",
... | 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 find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | \dfrac{1}{12} | alternative | [
"To find the maximum value of the expression \\(\\sum_{i=1}^{n} \\left( x_i^4 - x_i^5 \\right)\\) given that \\( \\sum_{i=1}^{n} x_i = 1 \\), we will explore different approaches and then compare them.\n\n### Approach 1: Analyzing Individual Terms\n\nConsider the function \\( f(x) = x^4 - x^5 \\). We need to determ... | [
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": "## 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 find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | 24 | alternative | [
"Let's denote:\n- \\( A \\) as the number of Astoria bottles,\n- \\( C \\) as the number of Cola bottles,\n- \\( L \\) as the number of Lemonade bottles,\n- \\( S \\) as the number of Selters bottles.\n\nFrom the problem statement, we have these relationships:\n\n1. \\( A = 5C \\) (five times as many Astoria bottle... | [
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": "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 find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | B | alternative | [
"To solve this problem, we need to consider the geometric configuration and properties of equilateral triangles formed with one vertex at a fixed point \\( P \\) on the angle bisector of a \\( 120^\\circ \\) angle.\n\n### Step-by-Step Solution:\n\n1. **Understanding the Geometry:**\n - We have two rays forming a ... | [
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": "2. Find the minimum value of the expression for $a, b>0$\n\n$$\n\\frac{(2 a+2 a b-b(b+1))^{2}+\\left(b-4 a^{2}+2 a(b+1)\\right)^{2}}{4 a^{2}+b^{2}}\n$$"
},
{
"from": "assistant",
"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 find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | 1 | alternative | [
"To find the minimum value of the given expression:\n\n\\[ \\frac{(2a + 2ab - b(b+1))^2 + (b - 4a^2 + 2a(b+1))^2}{4a^2 + b^2}, \\]\n\nwe will first simplify the terms inside the numerator.\n\n### Step 1: Simplify the Numerator Terms\n\nLet's start with the first term:\n\\[ 2a + 2ab - b(b+1) = 2a + 2ab - b^2 - b. \\... | [
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": "Convert the base-7 number $305_{(7)}$ to a base-5 number."
},
{
"from": "assistant",
"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 find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | 1102_{(5)} | alternative | [
"First, let's convert the base-7 number \\( 305_{(7)} \\) to a decimal (base-10) number. We do this by expanding it according to its place values:\n\n\\[ 305_{(7)} = 3 \\cdot 7^2 + 0 \\cdot 7^1 + 5 \\cdot 7^0 \\]\n\nCalculating each term:\n\\[ 3 \\cdot 7^2 = 3 \\cdot 49 = 147 \\]\n\\[ 0 \\cdot 7^1 = 0 \\]\n\\[ 5 \\... | [
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": "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 find multiple answers for a question then deliberate over them saying \"Alternatively,\" between each answer you are deliberating on 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 an answer... | 50 | alternative | [
"Firstly, let's determine how many cards Malcom originally had before he gave any away.\n\nMalcom has 8 more cards than Brandon. Since Brandon has 20 cards:\n- Original amount = 20 + 8 = 28 cards\n\nNow, if Malcom ends up with 14 cards after giving away x% of his original cards, we need to figure out the value of x... | [
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 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 find multiple answers for a question then deliberate over them saying \"Alt(...TRUNCATED) | C | alternative | ["To solve this problem, we need to analyze the given conditions and determine the possible number o(...TRUNCATED) | [
false,
false
] | [
"",
""
] | {"api_url":"http://10.32.36.231:9080/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":"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 find multiple answers for a question then deliberate over them saying \"Alt(...TRUNCATED) | B | alternative | ["To solve for vector \\(\\overrightarrow{b}\\), we start from the given information:\n\n\\[ 2\\over(...TRUNCATED) | [
false,
false
] | [
"",
""
] | {"api_url":"http://10.32.36.231:9080/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":"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 find multiple answers for a question then deliberate over them saying \"Alt(...TRUNCATED) | 2^k | alternative | ["To prove that \\(1 + \\frac{1}{2} + \\frac{1}{3} + \\frac{1}{4} + \\ldots + \\frac{1}{2^n-1} > \\f(...TRUNCATED) | [
false,
false
] | [
"",
""
] | {"api_url":"http://10.32.36.231:9080/v1","backend":"litellm","chat_template_applied":true,"generatio(...TRUNCATED) | {
"backend": "litellm",
"model_name": "hosted_vllm/Qwen/Qwen2.5-7B-Instruct",
"n_responses": 2
} |
End of preview. Expand in Data Studio
README.md exists but content is empty.
- Downloads last month
- 3