prompt list | ground_truth string |
|---|---|
[
{
"content": "Let \\((x,y,z)\\) be an ordered triplet of real numbers that satisfies the following system of equations: \\[x+y^2+z^4=0, \\quad y+z^2+x^4=0, \\quad z+x^2+y^4=0.\\] If \\(m\\) is the minimum possible value of \\(\\lfloor x^3+y^3+z^3\\rfloor\\), find \\(m \\mod 2007\\).",
"role": "user"
}
] | 2006 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.11 s |
[
{
"content": "Evaluate the limit: $$\\lim_{n\\rightarrow\\infty}\\sqrt[n]{\\sum\\limits_{k=0}^{n} \\frac{(-1)^k}{k+1}\\cdot2^{n-k}\\cdot\\binom{n }{k}}$$",
"role": "user"
}
] | 2 |
[
{
"content": "Determine whether the following statement is true or false: Given a collection of subsets of real numbers $A_i \\subset \\mathbb{R}, i \\in \\mathbb{N}$, is it true that $$\\sup \\{\\sup A_i, i \\in \\mathbb N\\} = \\sup (\\cup_i A_i)?$$",
"role": "user"
}
] | True |
[
{
"content": "How many subfields of the finite field \\( \\mathbb{F}_{5^4} \\) are isomorphic to \\( \\mathbb{F}_{5^2} \\)?",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to 0^{+}} \\frac{\\arcsin(1-\\{x\\})\\arccos(1-\\{x\\})}{\\sqrt{2\\{x\\}}(1-\\{x\\})} \\] where \\(\\{\\cdot\\}\\) denotes the fractional part function.",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Union Company
Worksheet for the month of December 2007
| Number | Account Title | Adjusted Trial Balance (Debit) | Adjusted Trial Balance (Credit) | Income statement (Debit) | Income statement (Credit) | Balance sheet (Debit) | Balance sheet (Credit) |
|---|---|---|---|---|---|---|---|
| 101 | Cash | 500 | | | | 5... |
[
{
"content": "Given triangle \\( \\triangle ABC \\) with vertex \\( A(3, -1) \\), the equation of median \\( BE \\) is \\( 6x + 10y - 59 = 0 \\), and the equation of angle bisector \\( CF \\) is \\( x - 4y + 10 = 0 \\). Determine the slope of line \\( BC \\).",
"role": "user"
}
] | -\dfrac{2}{9} |
[
{
"content": "Consider the following greedy algorithm: Let \\( p(n) \\) be the number of unrestricted partitions of \\( n \\), with \\( p(0) = 1 \\). Start with two empty sets, Set 1 and Set 2. Place \\( p(n) \\) into Set 1. For each successive step \\( k = 1, 2, 3, \\ldots, n \\), place \\( p(n-k) \\) into the... | Yes |
[
{
"content": "Let $L$ and $M$ be lattices in $\\mathbb{C}$. Suppose $\\gamma,\\delta\\in\\mathbb{C}$ are non-zero and such that $\\gamma L\\subseteq M$ and $\\delta M\\subseteq L$. Does it then follow that $\\gamma L=M$?",
"role": "user"
}
] | No |
[
{
"content": "How many distinct Jordan canonical forms are possible for a $4 \\times 4$ complex matrix with the minimal polynomial $(x-3)^2(x-4)$?",
"role": "user"
}
] | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.59 rad |
[
{
"content": "Seven numbers form an increasing arithmetic progression. The sum of their cubes is zero, and the sum of their squares is 756. Determine the largest number in this progression.",
"role": "user"
}
] | 9\sqrt{3} |
[
{
"content": "Determine the maximum value of the positive number \\( r \\) such that the set \\( T = \\left\\{(x, y) \\mid x, y \\in \\mathbb{R}, \\text{ and } x^{2} + (y-7)^{2} \\leq r^{2} \\right\\} \\) is a subset of the set \\( S = \\{(x, y) \\mid x, y \\in \\mathbb{R}, \\text{ and for any } \\theta \\in \\... | 4\sqrt{2} |
[
{
"content": "Compute the limit \\( \\lim_{s \\to \\infty} \\int_0^1 \\left|\\cos(sx)\\right| \\, dx \\).",
"role": "user"
}
] | \dfrac{2}{\pi} |
[
{
"content": "Let $D$ be an integral domain and $S$ be a multiplicatively closed subset of $D$ that does not contain zero. Consider $D$ as a subring of $S^{-1}D$, which is further a subring of the fraction field of $D$. If for every $q \\in S^{-1}D$, there exists a monic polynomial $P_q(X) \\in D[X]$ such that ... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $6.03 |
[
{
"content": "In triangle $ABC,$ $\\angle A = 90^\\circ,$ $AC = 1,$ and $AB = 5.$ Point $D$ lies on ray $\\overrightarrow{AC}$ such that $\\angle DBC = 2 \\angle CBA.$ Compute $AD.$",
"role": "user"
}
] | \frac{37}{11} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2013: 21.78%
2014: 22.13%
2015: 20.78% |
[
{
"content": "In a triangle, determine the ratio of the distance from a vertex to the orthocenter to the distance from the circumcenter to the side opposite that vertex.",
"role": "user"
}
] | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 48.86 months |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.77% |
[
{
"content": "Determine whether the function \\( f(x,y) = \\begin{cases} xy \\sin\\left(\\frac{1}{x^2+y^2}\\right) & (x,y) \\neq (0,0) \\\\ 0 & (x,y)=(0,0) \\end{cases} \\) is differentiable at the point \\((0,0)\\).",
"role": "user"
}
] | Yes |
[
{
"content": "Calculate the remainder when \\( 37^{877} \\) is divided by 323.",
"role": "user"
}
] | 284 |
[
{
"content": "Let \\( P \\) be a non-zero projector. Determine whether the statement \\( ||P||_F \\geq 1 \\) holds true, with equality if and only if \\( P \\) is an orthogonal projector.",
"role": "user"
}
] | ||P||_F \geq 1 |
[
{
"content": "Find the smallest natural number that divides \\(2^n + 15\\) for some natural number \\(n\\) and can be expressed in the form \\(3x^2 - 4xy + 3y^2\\) for some integers \\(x\\) and \\(y\\).",
"role": "user"
}
] | 23 |
[
{
"content": "Evaluate the integral \\(\\int_{\\frac{\\pi}{6}}^{\\frac{\\pi}{3}}\\frac{3\\tan^2x+6\\tan x+11}{1+\\tan ^2x}dx\\) and express it in the form \\(\\frac{k\\pi+\\lambda}{6}\\). Determine the value of \\(k + \\lambda\\). \n\n\\(\\text{(A) } 10 \\hspace{1cm} \\text{(B) } 12 \\hspace{1cm} \\text{(C) } 1... | D |
[
{
"content": "Is the square root of the Gelfond-Schneider constant \\(2^\\sqrt{2}\\) transcendental?",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 37.6 L |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 713 N/m |
[
{
"content": "In the Cartesian coordinate system, consider the ellipse \\(C: \\frac{x^{2}}{27}+\\frac{y^{2}}{18}=1\\) with its right focus \\(F\\). A line \\(l\\) passing through \\(F\\) intersects the ellipse \\(C\\) at points \\(A\\) and \\(B\\). Determine if there exists a fixed point \\(P\\) on the \\(x\\)-... | (4, 0) |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\to\\infty} \\left(\\frac{x+1}{(x!)^{\\frac{1}{x-1}}}\\right) $$",
"role": "user"
}
] | e |
[
{
"content": "Does the space $L^1(\\mathbb{X})$, where $\\mathbb{X}$ is a measure space, have Schur's property, meaning that weak convergence implies strong convergence?",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 271955 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.5 feet per second |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 10.5 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 0.21 M |
[
{
"content": "Given the matrix representations of the imaginary unit \\(i=\\begin{pmatrix}0 & -1 \\\\ 1 & 0 \\end{pmatrix}\\), the dual numbers unit \\(\\epsilon=\\begin{pmatrix}0 & 1 \\\\ 0 & 0 \\end{pmatrix}\\), and the split-complex unit \\(j=\\begin{pmatrix}0 & 1 \\\\ 1 & 0 \\end{pmatrix}\\), determine if t... | Yes |
[
{
"content": "A 6-sided die is biased such that rolling a 1 is twice as likely as rolling any other number, and the probabilities for rolling 2, 3, 4, 5, and 6 are equal. Specifically, the probabilities are given by: \\( p(1) = \\frac{2}{7} \\) and \\( p(2) = p(3) = p(4) = p(5) = p(6) = \\frac{1}{7} \\). What i... | \dfrac{323}{20} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 20 cm |
[
{
"content": "Given a coin where the probability of landing heads is $p^2$, and $p$ is uniformly distributed over $[0,1]$, calculate the probability that $p < \\frac{1}{2}$ given that a head is observed when the coin is flipped.",
"role": "user"
}
] | \dfrac{1}{8} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $50.00 per direct labor hour |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1560 A |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Search, Mismatch |
[
{
"content": "In a complete and separable metric space $(X, \\mathrm{d})$, given an open set $U$ and a closed set $K \\subset U$, determine if there exists a Lipschitz function $f$ such that $f|_K = 1$ and $f|_{X \\setminus U} = 0$. Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 43.66% |
[
{
"content": "How many permutations of the set \\(\\{1, 2, \\.\\.\\., 8\\}\\) do not leave any even number in its original position?",
"role": "user"
}
] | 24024 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 510 N |
[
{
"content": "Determine whether the following statement is true or false: If a function $f: \\mathbb{R}^d \\to \\mathbb{R}$ is twice continuously differentiable and the gradient of $f$ is $L$-Lipschitz continuous, then the Hessian of $f$ has a bounded norm, i.e., $||\\nabla^2 f(x)|| \\leq L$ for all $x$. Provid... | True |
[
{
"content": "Evaluate the improper integral: \\[ I = \\lim_{n\\rightarrow \\infty}\\int_0^{2\\pi}{\\frac{\\cos nx}{x+1}}\\,\\text{d}x \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit: $$ \\lim_{n\\to\\infty}\\left[\\frac{1}{\\sqrt{n^2+2}}+\\frac{1}{\\sqrt{n^2+4}}+\\frac{1}{\\sqrt{n^2+6}} + \\dots + \\frac{1}{\\sqrt{n^2+2n}}\\right] $$",
"role": "user"
}
] | 1 |
[
{
"content": "If $x$ is real, compute the maximum integer value of\n\\[\\frac{3x^2 + 9x + 17}{3x^2 + 9x + 7}.\\]",
"role": "user"
}
] | 41 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4148 lb |
[
{
"content": "Does there exist a countable proper subset $S$ of $\\mathbb{Q}$ such that $\\mathbb{Q} \\setminus S$ is infinite but not dense in $\\mathbb{R}$?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the dimensions $n$ for which the existence of an $n \\times n$ complex matrix $A$ with $\\det(I-A^*A)<0$ implies that the operator norm of $A$ is greater than 1.",
"role": "user"
}
] | n \geq 1 |
[
{
"content": "Let \\( f: \\mathbb{R} \\to \\mathbb{R} \\) be a function that is Riemann integrable on any bounded interval and satisfies \\( \\lim_{x \\to \\infty} f(x) = 0 \\). Define \\( g(x) = \\int_{x}^{x+1} f(t) \\, dt \\). Prove that \\( \\lim_{x \\to \\infty} g(x) = 0 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4 ft/sec |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2205 J |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 92 km/hr |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | The genotype proportion method |
[
{
"content": "Evaluate the limit \\( \\displaystyle \\lim_{x \\to 0^+} \\frac{(\\sin x)^\\frac{1}{\\ln x}}{x^\\frac{1}{\\ln x}} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $40 |
[
{
"content": "Does the nonsingularity of a real $n \\times n$ matrix $A$ guarantee that $A^TA$ is positive definite? Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 112.7099 |
[
{
"content": "Determine the rate of convergence with respect to \\(\\epsilon\\) for the norm \\(\\|f_\\epsilon-f\\|_{L^1}\\), where \\(f_\\epsilon = \\phi_\\epsilon * f\\) and \\(\\phi_\\epsilon = (1/\\epsilon)\\phi(x/\\epsilon)\\) is a mollifier.",
"role": "user"
}
] | O(\epsilon) |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.48 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6Fe^(2+) \rightarrow 6Fe^(3+) + 6e^(-) |
[
{
"content": "Given a set of 6 distinct digits, how many valid sequences of six digit pairs can be generated? Each digit in the set can be used exactly twice, and each pair must consist of two different digits. Determine the total number of such sequences.",
"role": "user"
}
] | 67950 |
[
{
"content": "Evaluate the limit: \\( \\lim\\limits_{n \\to \\infty} \\frac{\\ln(n!)}{n} \\)",
"role": "user"
}
] | \infty |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1/sqrt(2) |
[
{
"content": "Given the sequence \\(\\{x_n\\}\\) with \\(\\lim_{n \\to \\infty} x_n = a\\), and the line \\(AA_n\\) defined by the points \\(A = (a, a^2)\\) and \\(A_n = (x_n, x_n^2)\\), let \\(a_n\\) be the abscissa of the intersection point of \\(AA_n\\) with the x-axis. Find \\(\\lim_{n \\to \\infty} a_n\\).... | \dfrac{a}{2} |
[
{
"content": "Find the number of spanning trees in the complete graph $K_{12}$ that have exactly two vertices with degree 6.",
"role": "user"
}
] | 16632 |
[
{
"content": "Given complex numbers with moduli $|a|=4$, $|b|=10$, and $|c|=1$, find the smallest possible value of $|a+b+c|$. Under what conditions does this minimum occur?",
"role": "user"
}
] | 5 |
[
{
"content": "A monkey starts at position 0 on the real number line at time 0. In each time step $t$ (where $t \\in \\{0, 1, 2, ...\\}$), the monkey moves right by 1 with probability $p$ and left by 1 with probability $1-p$, where $p \\in \\left[\\frac{1}{2}, 1\\right]$. What is the probability that the monkey ... | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 156.32 N |
[
{
"content": "Determine the number of integers \\( n \\), where \\( 1 \\leq n \\leq 2017 \\), such that the expression \\( 323 \\) divides \\( 20^n + 16^n - 3^n - 1 \\).",
"role": "user"
}
] | 1008 |
[
{
"content": "True or false: Every harmonic function on \\(\\Bbb C \\setminus \\{0\\}\\) has a harmonic conjugate.",
"role": "user"
}
] | B |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 6.96 kg |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.50 mol O2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.54 sec |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4900 |
[
{
"content": "Given the real numbers \\(\\alpha\\) and \\(\\beta\\) that satisfy the following system of equations:\n\\[\n\\begin{cases}\n\\alpha^{3} - 3\\alpha^{2} + 5\\alpha - 17 = 0 \\\\\n\\beta^{3} - 3\\beta^{2} + 5\\beta + 11 = 0\n\\end{cases}\n\\]\nfind the value of \\(\\alpha + \\beta\\).",
"role": "... | 2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 777.4 s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $46,946,410 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.68 |
[
{
"content": "Calculate the expression $E[X \\mid E[X \\mid Y]]$. Provide your answer in terms of $X$ and $Y$.",
"role": "user"
}
] | E[X \mid Y] |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 3.15 m |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 7.1e+27 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Machine X |
[
{
"content": "A function $g: \\mathbb{R} \\to \\mathbb{R}$ is defined by the equation\n\n$$ g(x) + g(y) + 2g(xy) = \\frac{g(xy)}{g(x+y)}$$\n\nGiven that $g(1) = 1$, determine the value of $g(2023)$. \\( \\boxed{} \\)",
"role": "user"
}
] | \dfrac{1}{6067} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 497.52 |
[
{
"content": "Given the joint probability density function of a bivariate random variable $(X,Y)$:\n\n$$f_{XY}(x,y) = \\frac{1}{\\sqrt{3 \\pi }} e^{-\\frac{2}{3} (x^2 - xy + y^2)}$$\n\nFind the mean of the random variable $X$. \\( \\mu_X = ? \\)",
"role": "user"
}
] | 0 |
[
{
"content": "Find the coefficient of $x^{52}$ in the expression:\n\n$$(x^{10} + x^{11} + \\ldots + x^{25})(x + x^2 + \\ldots + x^{15})(x^{20} + x^{21} + \\ldots + x^{45})$$",
"role": "user"
}
] | 204 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 9.23e+23 molecules |
[
{
"content": "Evaluate the double integral \\( I:=\\iint_{D} \\frac{x^2-y^2}{1+x^4+y^4} \\, \\mathrm{d}x \\, \\mathrm{d}y \\) where \\(D\\) is a bounded and closed domain in \\(\\mathbb{R}^2\\) that is symmetric with respect to the line \\(y=x\\). The distance between any boundary of \\(D\\) and the point \\((a... | 0 |
[
{
"content": "Given a function $f:\\mathbb{N}\\rightarrow\\mathbb{N}$ defined as follows:\n\n$$f(n)=\\left\\{ \\begin{array}{lcc} n-3 & if & n \\geq 1000 \\\\\nf(f(n+6)) & if & n < 1000 \\end{array} \\right\\}$$\n\nCalculate the exact value of $f(1)$. Provide your answer as a single integer.",
"role": "user... | 997 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | vertical |
[
{
"content": "Calculate the conditional covariance of $B_s$ and $B_t$ given $B_1$, where $B$ is a one-dimensional Brownian motion and $s, t \\in [0,1]$. Provide your answer as a function of $s$ and $t$.",
"role": "user"
}
] | \min(s, t) - st |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 85 mL |
[
{
"content": "What is the remainder when $9^{1995}$ is divided by 7?",
"role": "user"
}
] | 1 |
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