prompt list | ground_truth string |
|---|---|
[
{
"content": "Given that the function $f(x,y)$ satisfies Laplace's equation \\( \\frac{\\partial^2 f}{\\partial x^2} + \\frac{\\partial^2 f}{\\partial y^2} = 0 \\), determine whether the function \\( f\\left(\\frac{x}{x^2+y^2}, \\frac{y}{x^2+y^2}\\right) \\) also satisfies Laplace's equation.",
"role": "use... | Yes |
[
{
"content": "Compute the residue of the function \\( \\frac{(\\sin(z))^2}{(\\sinh(z))^5} \\) at \\( z = 0 \\).",
"role": "user"
}
] | -\dfrac{7}{6} |
[
{
"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... | 97% |
[
{
"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... | 0.087 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... | City U |
[
{
"content": "Determine the number of roots of the equation $\\sin x = \\frac{x}{100}$.",
"role": "user"
}
] | 63 |
[
{
"content": "Let $X$ and $Y$ be independent geometric random variables with parameter $p$. Compute $E(X|X+Y=k)$ for all $k = 2,3,4,...$. Provide your answer as a function of $k$ and $p$.",
"role": "user"
}
] | \dfrac{k}{2} |
[
{
"content": "Let \\( G \\) be an abelian group with a collection of subgroups \\( H_i \\) for \\( i \\in \\mathbb{Z} \\), satisfying the following conditions: Each \\( H_i \\) is a complete topological group, \\( H_i \\supset H_{i+1} \\), \\( G = \\bigcup_{i \\in \\mathbb{Z}} H_i \\), and \\( 0 = \\bigcap_{i \... | 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... | $43.72 |
[
{
"content": "Determine whether the symmetric group $S_{10}$ has a subgroup with index 4. Answer with True or False.",
"role": "user"
}
] | False |
[
{
"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... | 8.5 m |
[
{
"content": "Find the maximum value of \\(|z^n + a|\\) for complex numbers \\(z\\) with \\(|z| \\leq 1\\), where \\(n\\) is a positive integer and \\(a\\) is a complex number.",
"role": "user"
}
] | 1 + |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... | 14.5% |
[
{
"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... | Tennis Shoe |
[
{
"content": "Is a linear function \\(f:\\{\\lambda a+(1-\\lambda)b:0\\leq\\lambda \\leq 1\\} \\to \\mathbb{R}\\), where \\(V\\) is a real vector space and \\(a,b\\in V\\) with \\(a\\neq b\\), necessarily continuous?",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x\\to0^+} \\left(\\frac{x^{\\sin(x)}-1}{x}\\right) \\]",
"role": "user"
}
] | -\infty |
[
{
"content": "Compute the expected value of $X_{n+1}$, given that $X_n = X_0 e^{\\mu S_n}$, where $X_0 > 0$, $S_n$ is a symmetric random walk, and $\\mu > 0$.",
"role": "user"
}
] | X_n \cosh(\mu) |
[
{
"content": "Consider a sequence of 58 terms defined as $P+n$, where $P$ is the product of all prime numbers less than or equal to 61, and $n$ takes values from 2 to 59 in succession. Determine the number $N$ of primes in this sequence.",
"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... | negative x-axis |
[
{
"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... | $26,270.98 |
[
{
"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... | 11.36 Km |
[
{
"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... | 44.8 L |
[
{
"content": "Calculate the limit, if it exists and is non-zero, for the following expression as \\(x\\) approaches 0: \n\\[\\lim_{x\\to0}\\frac{\\int_0^{x^2}\\frac{\\sin(t)-bt}{t}dt}{(e^x-1)^2}\\]",
"role": "user"
}
] | 1 - b |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0^+}\\frac{x^{(\\sin x)^x}-(\\sin x)^{x^{\\sin x}}}{x^3}. \\]",
"role": "user"
}
] | \dfrac{1}{6} |
[
{
"content": "Solve the system of equations for $m=1$:\n\\[x^{x+y} = y^m\\]\n\\[y^{x+y} = x^{2m} \\cdot y^m\\]",
"role": "user"
}
] | (1, 1) |
[
{
"content": "Calculate the volume enclosed by the surfaces $x^2+z^2=4$, $y=z$, and $y+z=4$ using a triple integral in cylindrical coordinates.",
"role": "user"
}
] | 16\pi |
[
{
"content": "Evaluate the integral \\( \\int_0^1 \\ln^n(x) \\, dx \\).",
"role": "user"
}
] | (-1)^n n! |
[
{
"content": "Calculate the area enclosed by the curve \\( r = 1 + \\sin\\theta \\) and outside the curve \\( r = 2\\sin\\theta \\) using double integrals in polar coordinates.",
"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... | $167,000 |
[
{
"content": "Determine whether the following statement about the Fermat primality test is correct:\n\nFor all integers $b$, if $n$ is a prime number and $(b,n)=1$, then $b^{n-1} \\equiv 1 \\pmod{n}$. The contrapositive is that if $b^{n-1} \\not\\equiv 1 \\pmod{n}$, then either $n$ is not prime or $(b,n) \\neq ... | Correct |
[
{
"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... | $1,194,192.47 |
[
{
"content": "Does there exist a function that is discontinuous at every point in its domain?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether there exists a function \\( f: (-\\delta, \\delta) \\to \\mathbb{R} \\) that satisfies the following conditions for a real number \\( \\delta > 0 \\):\n\n1. \\( f \\) is differentiable on \\((-\\delta, \\delta)\\).\n2. The second derivative \\( f''(0) \\) exists.\n3. There exists... | 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... | 0.96 |
[
{
"content": "Determine whether there exist two rational numbers, \\( p \\) and \\( q \\), such that \\( e^p = q \\).",
"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... | 25 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... | $159.31 |
[
{
"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... | 6910581.6 lb |
[
{
"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... | 33.66 m/s^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... | 11.14 rev |
[
{
"content": "Is it possible to arrange 105 delegates from 35 countries around a circular table such that no two delegates from the same country are seated next to each other?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine all real numbers \\(x\\) for which the series \\(\\sum_{n=1}^\\infty \\left(1+\\frac{1}{2}+\\cdots+\\frac{1}{n}\\right)\\frac{\\sin nx}{n}\\) converges.",
"role": "user"
}
] | \mathbb{R} |
[
{
"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... | 9.3 A |
[
{
"content": "Find all pairs of prime numbers \\((p, q)\\) such that the expression \\(p^{q+1} + q^{p+1}\\) is a perfect square.",
"role": "user"
}
] | (2, 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... | Product A: $64.89
Product B: $92.25 |
[
{
"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... | 2.8e2 min |
[
{
"content": "Compute\n\\[\\sum_{1 \\le a < b < c} \\frac{1}{2^a 3^b 5^c}.\\](The sum is taken over all triples $(a,b,c)$ of positive integers such that $1 \\le a < b < c.$)",
"role": "user"
}
] | \frac{1}{1624} |
[
{
"content": "Determine the number of subfields of a finite field with $2^{36}$ elements.",
"role": "user"
}
] | 9 |
[
{
"content": "Given the sequences\n\\[a_n = \\binom{n}{0} + \\binom{n}{3} + \\binom{n}{6} + \\dots\\]\n\\[b_n = \\binom{n}{1} + \\binom{n}{4} + \\binom{n}{7} + \\dots\\]\n\\[c_n = \\binom{n}{2} + \\binom{n}{5} + \\binom{n}{8} + \\dots\\]\nfind the value of\n\\[a_n^2 + b_n^2 + c_n^2 - a_nb_n - b_nc_n - c_na_n\\]... | 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... | 594.64 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... | 2000 eV |
[
{
"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... | 5.65e+24 atoms |
[
{
"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... | CO + 3/2H_2 -> CH_2OH |
[
{
"content": "In a game played on a $100 \\times 100$ board, Petya, Vasya, and Tolya take turns painting the boundary cells of the board. The rules are: a cell cannot be painted if it is adjacent to an already painted cell, and a cell cannot be painted if it is symmetrical to an already painted cell with respec... | 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... | 2.6e-9 |
[
{
"content": "Find the limit: \\[ \\lim_{n \\rightarrow \\infty} \\dfrac{2^{2n}(n!)^2}{(2n+1)!} \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Let $a$, $b$, and $c$ be positive real numbers with $a < b < c$ such that $a + b + c = 12$, $a^2 + b^2 + c^2 = 50$, and $a^3 + b^3 + c^3 = 216$. Find the value of $a + 2b + 3c$.",
"role": "user"
}
] | 26 |
[
{
"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... | y = 0.4610cos(4.33t) |
[
{
"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... | -26.4 kJ |
[
{
"content": "Consider a compact metric space $X$ and a closed relation $\\sim$ on $X$. The quotient space $X/\\sim$ is compact Hausdorff and metrizable. Is the Hausdorff metric on the equivalence classes $[x] \\in X/\\sim$, which are compact subsets of $X$, a metric compatible with the topology of $X/\\sim$?",... | No |
[
{
"content": "Does every commutative monoid admit a translation-invariant measure when equipped with the Borel $\\sigma$-algebra $\\mathcal B(T)$ derived from its canonical pre-order topology?",
"role": "user"
}
] | No |
[
{
"content": "What real number is equal to the expression $2 + \\frac{4}{1 + \\frac{4}{2 + \\frac{4}{1 + \\cdots}}}$, where the $1$s and the $2$s alternate?",
"role": "user"
}
] | 4 |
[
{
"content": "Determine the number of elements in the splitting field of the polynomial \\((x^3 + x - 1)(x^4 + x - 1)\\) over \\(\\mathbb{F}_3\\).",
"role": "user"
}
] | 81 |
[
{
"content": "Determine the maximum value of the function \\( g(a) = \\sqrt[3]{a + \\frac{a+1}{3}\\sqrt{\\frac{8a-1}{3}}} + \\sqrt[3]{a - \\frac{a+1}{3}\\sqrt{\\frac{8a-1}{3}}} \\) for \\( a \\geq \\frac{1}{8} \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Let $X_{1}, X_{2}, \\ldots, X_{n}$ be independent and identically distributed random variables with finite expected values. Given that $(X_{1}+X_{2}+ \\ldots + X_{n}) = x$ and assuming $f_{(X_{1}+X_{2}+ \\ldots + X_{n})}(x) \\neq 0$, determine $\\mathbb{E}[X_{1}|(X_{1}+X_{2}+ \\ldots + X_{n})=x]$.... | \dfrac{x}{n} |
[
{
"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... | x = 5sqrt(m/k) |
[
{
"content": "How many unique permutations are possible for a 3x3x3 cube where each of the 27 smaller cubes has a distinct number, considering that simple rotations of the entire cube should not be counted as different permutations?",
"role": "user"
}
] | \dfrac{27!}{24} |
[
{
"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... | 0.2 m/s^2 to the left |
[
{
"content": "A line goes through point $A(9, 1)$, point $B(19, k)$ and point $C(7, 0)$. What is the value of $k$?",
"role": "user"
}
] | 6 |
[
{
"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... | 148 |
[
{
"content": "Let $M$ be an embedded submanifold of dimension $k$ in $\\Bbb R^n$. Given coordinates $u^1, \\dots, u^k$ for a region of $M \\subset \\Bbb R^n$, the inclusion map $M \\hookrightarrow \\Bbb R^n$ determines $n$ smooth functions $x_1(u^1, \\dots, u^k), \\dots, x_n(u^1, \\dots, u^k)$. Define $\\vec{x}... | Yes |
[
{
"content": "Determine the number of 9-digit positive integers that do not contain any substring of three consecutive repeating digits.",
"role": "user"
}
] | 843160671 |
[
{
"content": "Evaluate the limit: $$\\lim_{x\\rightarrow0} \\left(\\frac{\\sin x}{x}\\right)^{\\frac{1}{\\cos x}}$$",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{x \\to 0} \\left( \\left( \\dfrac{1-x}{e} \\right) ^ { \\dfrac{1}{x} } \\right) ^ { \\dfrac{1}{\\sin x} } \\]",
"role": "user"
}
] | 0 |
[
{
"content": "Container I holds 8 red balls and 4 green balls; containers II and III each hold 2 red balls and 4 green balls. A container is selected at random and then a ball is randomly selected from that container. What is the probability that the ball selected is green? Express your answer as a common fract... | \frac{5}{9} |
[
{
"content": "Evaluate the limit: $$ \\lim_{(x,y) \\to (1,0)} \\frac{(x-1)^2 \\ln x}{(x-1)^2 + y^2} $$",
"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... | 10007.43 m/s^2 |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to 0^+} \\left [ \\ln({x^3+2x^2+x})+ \\frac{2}{x} \\right ]$$",
"role": "user"
}
] | \infty |
[
{
"content": "If \\( \\alpha, \\beta, \\gamma \\) are the roots of the equation \\( x^3 + (a^4 + 4a^2 + 1)x = x^2 + a^2 \\), find the minimum value of the expression \\( \\frac{\\alpha}{\\beta} + \\frac{\\beta}{\\alpha} + \\frac{\\gamma}{\\alpha} + \\frac{\\alpha}{\\gamma} + \\frac{\\beta}{\\gamma} + \\frac{\\g... | 3 |
[
{
"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... | $34,320 |
[
{
"content": "In triangle $ABC$, which is scalene, points $P$ and $Q$ are located on segment $BC$ such that $P$ is between $B$ and $Q$. The distances are $BP=21$, $PQ=35$, and $QC=100$. If $AP$ and $AQ$ trisect $\\angle A$, express $\\frac{AB}{AC}$ in the form $\\frac{p\\sqrt{q}}{r}$, where $p$ and $r$ are rela... | 92 |
[
{
"content": "If \\(M\\) is a linear operator on \\(\\mathbb{R}^3\\) with unique and real eigenvalues \\(\\lambda_1 < \\lambda_2 < \\lambda_3\\), and there exists a vector \\(x \\in \\mathbb{R}^3 \\setminus \\{0\\}\\) such that \\(\\lim_{n \\to \\infty} ||M^n x|| = 0\\), what are the possible values of \\(\\lam... | (-\infty, 1) |
[
{
"content": "Let $G$ be a group, and $H_1, H_2$ be subgroups of $G$ with $|H_1|=15$ and $|H_2|=25$. If $G$ is not cyclic, determine the order of $|H_1 \\cap H_2|$.",
"role": "user"
}
] | 5 |
[
{
"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... | 374.468 mL |
[
{
"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... | 16800 |
[
{
"content": "Evaluate the limit using the concept of Riemann sums: $$\\lim_{n \\to \\infty}\\sum_{k=0}^n \\frac{\\sqrt{n}}{n+k^2}$$",
"role": "user"
}
] | \dfrac{\pi}{2} |
[
{
"content": "Consider a quadratic equation \\(p(x) = ax^2 + bx + c = 0\\) with real coefficients that has purely imaginary roots. Determine the nature of the roots of the equation \\(p(p(x)) = 0\\). Choose the correct option:\n\n(A) only purely imaginary roots\n(B) all real roots\n(C) two real and two purely i... | D |
[
{
"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... | N3H16PO4 |
[
{
"content": "Evaluate the exterior $2$-form $\\theta = \\sum_{i=1}^{n-1} x_i \\wedge x_{i+1}$ on $\\mathbb{R}^n$ using the vectors $A = (1, 1, 1, \\dots, 1)$ and $B = (-1, 1, -1, \\dots, (-1)^n)$. Compute the result.",
"role": "user"
}
] | 1 + (-1)^n |
[
{
"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... | $1.70 |
[
{
"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... | -5.3e+4 N |
[
{
"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... | 8.57 * 10^22 |
[
{
"content": "Given that $f(k)$ is a strictly increasing function from $\\mathbb{Z}^+$ to $\\mathbb{Z}^+$ satisfying $f(f(k)) = 3k$, find the sum $f(1) + f(9) + f(99)$. Provide your answer as a single integer.",
"role": "user"
}
] | 200 |
[
{
"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... | 1.44 |
[
{
"content": "Let $f:\\mathbb{C} \\to \\mathbb{C}$ be an entire function satisfying $|f(z)| \\leq 100 \\ln |z|$ for $|z| \\geq 2$, and assume that $f(i) = 2i$. Determine the value of $f(1)$. \\( \\boxed{?} \\)",
"role": "user"
}
] | 2i |
[
{
"content": "The length of the longer side of rectangle $R$ is $10$ percent more than the length of a side of square $S.$ The length of the shorter side of rectangle $R$ is $10$ percent less than the length of a side of square $S.$ What is the ratio of the area of rectangle $R$ to the area of square $S?$ Expre... | \frac{99}{100} |
[
{
"content": "What is the result of \\( \\infty - 1 \\) in the Riemann sphere number system?",
"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... | 0.98 |
[
{
"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... | 0.075 M |
[
{
"content": "Find the quadratic function $f(x) = x^2 + bx + c$, where $b, c \\in \\mathbb{R}$, such that $f(x)$ is a factor of both $x^4 + 6x^2 + 25$ and $3x^4 + 4x^2 + 28x + 5$. Determine the expression for $f(x)$. \\( \\text{Express your answer in the form } f(x) = x^2 + bx + c. \\)",
"role": "user"
}
... | x^2 - 2x + 5 |
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