prompt list | ground_truth string |
|---|---|
[
{
"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... | $7,044.42 |
[
{
"content": "Determine the number of homomorphisms $\\phi: S_5 \\to C_5$.",
"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... | $241.73 |
[
{
"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... | $35,000 |
[
{
"content": "Determine the limit of the ratio between $N$ and the number of digits of $X$ in the equation $A^N = X$, where $A$ is a positive integer greater than 1 and $N$ is a positive integer. Verify if the first five digits of this limit are $3.3219$.",
"role": "user"
}
] | 3.3219 |
[
{
"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... | 2.47 |
[
{
"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... | -9,399 |
[
{
"content": "Consider the cubic equation \\(x^3 - ax + b = 0\\), where \\(a\\) and \\(b\\) are positive real numbers, and all roots are real. Let \\(\\alpha\\) be the root with the smallest absolute value. Determine the range of \\(\\alpha\\) from the following options:\n\n(A) \\(\\frac{2b}{3a} < \\alpha \\leq... | 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... | 17.4 V |
[
{
"content": "Given a function $f: \\mathbb{R} \\to \\mathbb{R}$, assume the following conditions hold:\n1. For every $a \\in \\mathbb{R}$ and for $k=n$ (or for any $k \\geq 0$ if $n=+\\infty$), there exist real numbers $c_0(a), \\ldots, c_k(a)$ such that\n \\[ f(x) = c_0(a) + c_1(a)(x-a) + \\frac{1}{2}c_2(a)... | 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... | 1.67e8 m/s |
[
{
"content": "Determine whether it is possible to construct a $C^\\infty$ function $g(x)$ such that $\\left|{\\frac {d^{k}g}{dx^{k}}}(0)\\right| = h(k)$ for any given function $h(k)$. Provide a justification for your answer.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether the following limit exists:\n\\[\\lim_{x\\to +\\infty}\\dfrac {\\cos^5x\\sin^5x} {x^8\\sin^2x-2x^7\\sin x\\cos^2x+x^6\\cos^4x+x^2\\cos^8x}\\]",
"role": "user"
}
] | 0 |
[
{
"content": "Let $m$ and $n$ be positive integers such that $x = m + \\sqrt{n}$ is a solution to the equation \\(x^2 - 10x + 1 = \\sqrt{x}(x + 1)\\). Find the value of \\(m + n\\).",
"role": "user"
}
] | 55 |
[
{
"content": "Let $A$ be a random variable uniformly distributed over the interval $(0, 2)$, and $B$ be a random variable uniformly distributed over the interval $(1, 3)$. Define $W = \\min(A, B)$ and $Z = \\max(A, B)$. Find the covariance $\\text{Cov}(W, Z)$. Express your answer as a single number.",
"role... | \dfrac{25}{576} |
[
{
"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... | -2.78e+3 m/s^2 |
[
{
"content": "If the length of a cycloid is 4 times the diameter of the rotating circle, determine how many times the area under the arch of the cycloid is compared to the area of the rotating circle.",
"role": "user"
}
] | 3 |
[
{
"content": "Given the 0-form \\(\\omega = xy \\, dx + 3 \\, dy - yz \\, dz\\), directly compute \\(d(d\\omega)\\) and verify that it equals zero.",
"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... | 90 degrees |
[
{
"content": "Determine whether the following statement is true or false: If a function $f$ is analytic and nowhere zero in the domain $D = \\{z : \\Re z < 2019 \\}$, then $\\log |f|$ is harmonic in $D$. Provide a justification for your answer.",
"role": "user"
}
] | A |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{\\pi} \\cos^4(x + \\sin 3x) \\, dx \\).",
"role": "user"
}
] | \dfrac{3\pi}{8} |
[
{
"content": "Let $m \\ge 3$ be an integer and let $S = \\{3,4,5,\\ldots,m\\}$. Find the smallest value of $m$ such that for every partition of $S$ into two subsets, at least one of the subsets contains integers $a$, $b$, and $c$ (not necessarily distinct) such that $ab = c$.",
"role": "user"
}
] | 243 |
[
{
"content": "Determine the number of ways to distribute 7 distinct objects into 3 indistinguishable boxes such that each box contains at least one object.",
"role": "user"
}
] | 301 |
[
{
"content": "Evaluate the integral \\( \\int_0^1 \\int_x^1 \\frac{\\cos(y)}{y} \\, dy \\, dx \\). Determine if the integral converges or not.",
"role": "user"
}
] | \sin(1) |
[
{
"content": "Determine the number of positive integers \\( k \\) not exceeding 2020 such that for any positive integer \\( n \\), the expression \\( 3^{(k-1) n+1} \\) does not divide \\( \\left(\\frac{(k n)!}{n!}\\right)^{2} \\).",
"role": "user"
}
] | 7 |
[
{
"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... | 5.51e-21 |
[
{
"content": "Evaluate the integral \\( \\displaystyle \\int^{1}_{-1}\\frac{x^3}{\\sqrt{1-x^2}}\\ln\\left(\\frac{1+x}{1-x}\\right)dx \\).",
"role": "user"
}
] | \dfrac{5\pi}{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... | H_2S + Cl_2 -> 2Cl^- + S + 2H^+ |
[
{
"content": "Let \\( f: \\mathbb{R} \\to \\mathbb{R} \\) be defined as \\( f(x) = 8x^3 + 3x \\). Given that \\( f \\) is continuous, strictly increasing, and surjective, compute the following limit:\n\\[ \\lim_{x \\to \\infty} \\frac{f^{-1}(8x) - f^{-1}(x)}{x^{1/3}}. \\]",
"role": "user"
}
] | \dfrac{1}{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... | 1.154 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... | 10.5 g |
[
{
"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 |
[
{
"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... | 7.38 m/s |
[
{
"content": "Determine whether there exists an additive function on the real numbers that is unbounded everywhere.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the number of real solutions to the equation\n\\[\\frac{1}{x - 1} + \\frac{2}{x - 2} + \\frac{3}{x - 3} + \\dots + \\frac{100}{x - 100} = x.\\]",
"role": "user"
}
] | 101 |
[
{
"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... | 3.23 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... | 19.68% |
[
{
"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... | $229 |
[
{
"content": "Find a function \\( g(z) \\) that satisfies the following conditions:\n\n- \\( g(z) \\) is continuous on the closed disk \\( |z| \\leq 1 \\)\n- \\( g(z) \\) is holomorphic on the open disk \\( |z| < 1 \\)\n- \\( g(0) = 1 \\)\n- The imaginary part of \\( g(z) \\) is less than or equal to 0 for all ... | 1 |
[
{
"content": "Determine whether the vector $A^Tb$ always belongs to the column space of $A^TA$, regardless of the rank of $A^TA$. 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... | 186.67 m/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... | 80 km/h |
[
{
"content": "Find a function \\( f(x) \\) that is defined for all \\( x \\), is nonzero at some point, and satisfies the equation \\( f(x) f(y) = f(x-y) \\) for all \\( x, y \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Compute the complex integral \\( \\int_{|z|=1} \\frac{1}{z^2+1} \\, dz \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether the series \\(\\sum_{k=1}^\\infty \\frac{1}{4^k(2k)}\\binom{2k}{k}\\) converges to \\(\\ln 2\\).",
"role": "user"
}
] | \ln 2 |
[
{
"content": "Given the joint probability density function:\n\n$$ f_{X,Y}(x,y) = \\left\\{ \\begin{array}{ccc}\n\\frac{1}{x}, & 0 < y < x, & 0< x< 1 \\\\\n0, & \\text{otherwise} &\n\\end{array} \\right. $$\n\nCalculate the variance of the random variable $Y$. \\( \\text{Var}(Y) \\)",
"role": "user"
}
] | \dfrac{7}{144} |
[
{
"content": "Find all solutions to the initial value problem (IVP) given by the differential equation \\( \\dot{x} = x^{2023} - x^{2022} \\) with the initial condition \\( x(0) = 1 \\).",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the asymptotic behavior of the probability that a randomly chosen monic polynomial of large degree $n$ in $\\mathbb{F}_p[x]$ is irreducible. This probability can be expressed as \\(\\lim_{n\\to\\infty}\\frac{N_p(n)}{p^n},\\) where \\(N_p(n)=\\frac{1}{n}\\sum_{d|n}p^d\\mu\\left(\\frac{n}{d... | 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... | 1.2e6 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... | 6.99 |
[
{
"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... | 121.47 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... | 8.5 nC |
[
{
"content": "Evaluate the surface integral \\( \\int F \\cdot \\text{d}S \\) for the vector field \\( F = [2y + 3, xz, yz - x] \\), where \\( S \\) is the surface of a cylinder with unit radius centered around the origin, and \\( -1 < z < 1 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit \\( \\lim_{n \\to \\infty} \\dfrac{1}{n^2} \\sum_{k=1}^{n-1} k \\cdot \\left \\lfloor x + \\dfrac{n-k-1}{n} \\right \\rfloor \\) to three decimal places, where \\( x = \\sqrt{2015} \\).",
"role": "user"
}
] | 22.395 |
[
{
"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... | 2.41 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... | 19 |
[
{
"content": "Determine the number of injective functions from the set of natural numbers \\( \\mathbb{N} \\) to itself.",
"role": "user"
}
] | 2^{\aleph_0} |
[
{
"content": "Given that the random variable X is uniformly distributed between [-3, 3], determine the optimal value of a that maximizes the amount of cash at the end of 50 rounds in the casino game.",
"role": "user"
}
] | 0 |
[
{
"content": "Calculate the limit: \\[ \\lim_{{x \\to 2}} \\left(2 e^{x-2} - 1\\right)^{\\frac{3x+2}{x-2}} \\]",
"role": "user"
}
] | e^{16} |
[
{
"content": "Evaluate the infinite series \\( \\sum_{n=1}^{\\infty} \\tan^{-1}\\frac{2}{n^2} \\).",
"role": "user"
}
] | \dfrac{3\pi}{4} |
[
{
"content": "Evaluate the limit: \\[ \\lim _{x \\rightarrow 0} \\dfrac{2f(x)-f(2x)}{x-f(x)} \\] where \\( f(x) = \\int _0^x \\dfrac{\\sin t}{t} dt \\).",
"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... | 613.62 N |
[
{
"content": "Calculate the limit: $$ \\lim_{t\\to \\infty}\\frac{1}{t^2}\\int_0^t \\ln(e^x+x^2)\\,dx $$",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Find all harmonic functions on \\(\\mathbb{R}^2\\) of the form \\(f(x^2+y^2)\\), where \\(f\\) is a \\(C^2\\) class function.",
"role": "user"
}
] | C |
[
{
"content": "Let $P$ be a nonempty polyhedron in $\\mathbb{R}^n$, and consider the following sets for all $i \\in I \\subseteq \\{1,\\dots,n\\}$ with $l_i, u_i \\in \\mathbb{R}$:\n\n1. Feasible region: $F := P \\cap \\{x \\in \\mathbb{R}^n \\mid l_i \\leq x_i \\leq u_i, \\ x_i \\in \\mathbb{Z}\\}$\n2. Unconstr... | Yes |
[
{
"content": "Find the volume of the solid region enclosed by the surfaces $x-y+z=6$, $x+y=2$, $x=y$, $y=0$, and $z=0$ without using a triple integral.",
"role": "user"
}
] | \dfrac{16}{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... | 0.49 m/s^2 |
[
{
"content": "Evaluate the integral \\( \\int_{|z| = 3}\\frac{\\exp(-z)}{z^2}dz \\) using the residue theorem.",
"role": "user"
}
] | -2\pi i |
[
{
"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... | 18935 years |
[
{
"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... | 318.4ms^-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... | 4.92e-21 J |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{1} \\frac{1}{x+\\sqrt{1-x^2}} \\, dx \\).",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"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... | 91.7 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... | 19.42 m |
[
{
"content": "Find the value of the limit: $$\\lim_{x \\to \\infty}\\frac{e^{e^x}}{e^{x^3}}.$$",
"role": "user"
}
] | \infty |
[
{
"content": "Consider the vector space $V = \\{p(x) \\in F[x] \\mid \\deg(p(x)) \\le n\\}$, where $F$ is a field. Let $T : V \\to V$ be the differentiation operator defined by $T(p(x)) = p'(x)$. Determine whether the only eigenvalue of $T$ is $\\lambda = 0$.",
"role": "user"
}
] | 0 |
[
{
"content": "Given a real-valued harmonic function $u$ on the complex plane $\\mathbb{C}$, consider the function $g: \\mathbb{R}^2 \\to \\mathbb{R}$ defined by \\[ g(x,y) = \\int_0^{2\\pi} u(e^{i\\theta}(x+iy)) \\sin \\theta \\,d\\theta. \\] Determine which of the following statements is true about $g$:\n\n(A)... | A |
[
{
"content": "Given a $12$-cycle permutation $\\sigma = (1, 2, \\dots, 12)$, determine the conditions under which $\\sigma^i$ is also a $12$-cycle. Consider the relationship between the order of a permutation and its cycle structure.",
"role": "user"
}
] | \gcd(i, 12) = 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... | 8.856e23 molecules |
[
{
"content": "Find a nontrivial unit polynomial \\( p(x) \\) in \\( \\mathbb{Z}_4[x] \\) such that \\( \\deg p(x) > 1 \\).",
"role": "user"
}
] | 1 + 2x^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... | 0.337 |
[
{
"content": "Let $S$ be the sum of all positive integers $n$ such that $n^2+12n-2007$ is a perfect square. Find the remainder when $S$ is divided by $1000.$",
"role": "user"
}
] | 464 |
[
{
"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... | $249.41 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{j \\rightarrow +\\infty} \\left(I + \\frac{A}{j}\\right)^j, \\] where \\( A \\) is an \\( n \\times n \\) matrix.",
"role": "user"
}
] | e^A |
[
{
"content": "Let \\((a_n)_n\\) be a convergent sequence. Determine the value of \\( \\lim_{n \\to \\infty} n(a_{n+1} - a_n) \\) if it exists.",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the contour integral \\( \\oint_C \\frac{z^2+1}{e^{\\frac {z}{10}}-1}dz \\), where \\( C \\) is the unit circle traversed counterclockwise.",
"role": "user"
}
] | 20\pi i |
[
{
"content": "Given a $10 \\times 10$ matrix $A = [a_{ij}]$ with the following properties:\n\n1. The set of elements $\\{a_{ij} \\mid 1 \\le i, j \\le 10\\} = \\{1, 2, \\ldots, 100\\}$.\n2. For any $p, q \\in \\mathbb{N}$ where $1 \\le p, q \\le 10$, the sum of the elements in each column $\\sum_{i=1}^{10} a_{i... | \dfrac{2}{101} |
[
{
"content": "Evaluate the integral: $$\\int_{0}^{\\infty} \\frac{\\cos(2x) - 1}{x^2} \\, dx$$",
"role": "user"
}
] | -\pi |
[
{
"content": "Find the value of $x \\in [-1.5, 3]$ such that the area of the triangle formed by the points $A=(-1.5, 2.25)$, $B=(3, 9)$, and $C=(x, x^2)$ on the parabola $y=x^2$ is maximized.",
"role": "user"
}
] | \dfrac{3}{4} |
[
{
"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... | 5.1e-3 g |
[
{
"content": "Evaluate the limit: \\[ \\lim _{n \\rightarrow \\infty} \\sum_{k>n+\\sqrt n}^\\infty \\frac{e^{-n}n^k}{k!} \\] using properties of Poisson random variables and an appropriate limit theorem.",
"role": "user"
}
] | 1 - \Phi(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... | 4 g/mol |
[
{
"content": "Find the limit as \\( n \\to \\infty \\) of the sequence defined by \\( a_{n+1} = \\frac{(a_n)^2}{6}(n+5)\\int_{0}^{3/n}{e^{-2x^2}} \\mathrm{d}x \\), with the initial term \\( a_1 = \\frac{1}{4} \\).",
"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... | 0.266 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... | 781 g |
[
{
"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... | 6.72e-5 J |
[
{
"content": "Determine which function is asymptotically greater as $n$ approaches infinity: $f(n) = 3^{2^n}$ or $g(n) = n! \\times n^3$.",
"role": "user"
}
] | f(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... | 7.59% |
[
{
"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... | 1.62e+3 L |
[
{
"content": "A coin is flipped eight times, and the sequence of heads and tails occurring is recorded. How many distinct sequences are possible?",
"role": "user"
}
] | 256 |
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