prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine the limit function \\(f(x)\\) as \\(n\\) approaches infinity for the sequence of functions \\(f_n(x)\\) defined on the interval \\([0, 3]\\) by:\n\\[\nf_n(x) = \\begin{cases}\n n^2x & \\text{if } 0 \\leq x \\leq \\frac{1}{n} \\\\\n n(2-nx) & \\text{if } \\frac{1}{n} < x \\leq \\frac{2}... | 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... | logos |
[
{
"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 degrees |
[
{
"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... | $416,873.89 |
[
{
"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... | 4886.6 m/s in the initial direction of flight |
[
{
"content": "Find the expected value of $e^{UV}$, where $U$ is an exponentially distributed random variable with rate 1, $U \\sim \\text{Exp}(1)$, and $V$ is a gamma distributed random variable with shape 2 and rate 1, $V \\sim \\text{Gamma}(2, 1)$. Assume $U$ and $V$ are independent.",
"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... | 5.34% |
[
{
"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 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... | $17,333 |
[
{
"content": "Calculate the distance between any two consecutive points of intersection on the spiral defined by the equation \\( r = \\theta \\) when it is intersected by a ray originating from the pole.",
"role": "user"
}
] | 2\pi |
[
{
"content": "Consider a continuous function \\( f : \\mathbb{R} \\rightarrow \\mathbb{R} \\). Let \\( A \\subset \\mathbb{R} \\) be defined as \\( A = \\{ y \\in \\mathbb{R} : y = \\lim f(x_n), \\text{ for some sequence } x_n \\rightarrow \\infty \\} \\). Determine which of the following statements about the s... | A |
[
{
"content": "Determine the values of \\( \\alpha > 0 \\) for which the sequence of functions \\( f_n(x) = n^{\\alpha} h(nx) \\) converges to 0 \\( \\lambda \\)-almost everywhere on \\( \\mathbb{R} \\), where \\( \\lambda \\) denotes the Lebesgue measure and \\( h \\in C^{\\infty}(\\mathbb{R}) \\) has compact s... | \alpha > 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... | -$191,538 |
[
{
"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... | 474.5 K |
[
{
"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... | 14616 |
[
{
"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... | 41.7 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... | The solubility of a substance can be altered by changing the polarity of the solvent, changing the temperature, or shifting the equilibrium by adding a competing agent. |
[
{
"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 km/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... | [HA](acetic acid) = 0.033M, [A-](sodium acetate)=0.102M |
[
{
"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... | 8.18 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... | 21.6 x 10^3 J |
[
{
"content": "Evaluate the surface integral \\(\\int_S z\\,dS\\) where \\(S=\\{(x,y,z):x^2+y^2+z^2=a^2, z\\geq 0, a>0\\}\\), a hemisphere of radius \\(a\\). Verify your result using the Gauss divergence theorem.",
"role": "user"
}
] | \pi a^3 |
[
{
"content": "One of the five faces of the triangular prism shown here will be used as the base of a new pyramid. The numbers of exterior faces, vertices and edges of the resulting shape (the fusion of the prism and pyramid) are added. What is the maximum value of this sum?\n\n[asy]\ndraw((0,0)--(9,12)--(25,0)-... | 28 |
[
{
"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... | 2.23 mol |
[
{
"content": "Determine if 2 is the only number that is both prime and highly composite, where a highly composite number is defined as a positive integer with more divisors than any smaller positive integer.",
"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... | 1301.4 m/s |
[
{
"content": "Consider the Sturm-Liouville problem given by the differential equation:\n\\[ y'' + \\lambda y = 0, \\]\nwith boundary conditions:\n\\[ y(0) = c\\pi y'(\\pi) - y(\\pi) = 0, \\]\nwhere \\( c > 1 \\). Determine the number of negative eigenvalues for this problem.",
"role": "user"
}
] | 0 |
[
{
"content": "Solve the system of congruences:\n\n$$\\begin{align} x & \\equiv 11 \\pmod{36}\\\\ x & \\equiv 7 \\pmod{40}\\\\ x & \\equiv 32 \\pmod{75} \\end{align}$$\n\nNote: Consider the shared factors in the moduli when applying the Chinese Remainder Theorem.",
"role": "user"
}
] | 407 |
[
{
"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... | 4e-23 m/s |
[
{
"content": "Calculate the difference between the sum of real roots of the function \\( f_{10}(x) = 1 - \\sum_{k=0}^{10} \\frac{x(1-x)\\cdots(k-x)}{(k+1)!} \\) and the sum of real roots of its derivative \\( f'_{10}(x) \\).",
"role": "user"
}
] | 6 |
[
{
"content": "Prove that if $f: S^1 \\to S^1$ is the map $z \\mapsto z^n$, then the induced map $f_*: H_1(S^1) \\to H_1(S^1)$ is given by multiplication by $n$.",
"role": "user"
}
] | 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... | 22 N |
[
{
"content": "Estimate the integral \\( \\int_0^{1/2} \\ln(1 + \\frac{x^2}{4}) \\, dx \\) with an error margin of at most \\(10^{-4}\\). Compute the power series of \\(\\ln(1 + \\frac{x^2}{4})\\) and use it to approximate the integral.",
"role": "user"
}
] | 0.0102 |
[
{
"content": "Suppose \\( x:[0,\\infty)\\to [0,\\infty) \\) is a continuous function with \\( x(0)=0 \\). If \\( \\left(x(t) \\right)^2\\leq 2+\\int_{0}^{t}x(u)du,~~~\\forall ~t\\geq 0, \\) determine which of the following is true for \\( x(\\sqrt{2}) \\):\n\n- \\( x(\\sqrt{2})\\in [0,2] \\)\n- \\( x(\\sqrt{2})... | B |
[
{
"content": "Let $A \\subset \\mathbb{R}^n$ be a Lebesgue null set, and let $\\mu$ be a positive $\\sigma$-finite measure such that $\\mu(A^c) = 0$ and $\\mu(A + r) = \\mu(A)$ for all $r \\in \\mathbb{R}^n$. Does this imply that $\\mu = 0$?",
"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... | -5.68 pC |
[
{
"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... | (13.26t - 8.1) rad/s^2 |
[
{
"content": "Evaluate the improper integral \\( \\int_{-1}^0 \\frac{e^{1/x}}{x^2} \\, dx \\). Determine whether the integral converges or diverges, and if it converges, find its value.",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"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... | 3/2 |
[
{
"content": "Let $g$ be a real-valued function defined on the interval $(-1,1)$ such that \\[ e^{-x}(g(x)-2e^x)=\\int_0^x \\sqrt{y^4+1}\\,dy \\] for all $x\\in (-1,1)$. Let $f$ be another function such that \\[ f(g(x))=g(f(x))=x. \\] Find the value of $f'(2)$. \\( \\)",
"role": "user"
}
] | \dfrac{1}{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... | 0.67 g/L |
[
{
"content": "Consider the matrix \\( A = \\begin{bmatrix}1 & \\tan x\\\\-\\tan x & 1\\end{bmatrix} \\). Define the function \\( f(x) = \\begin{vmatrix}A^{T}A^{-1}\\end{vmatrix} \\). Determine which of the following cannot be the value of \\( g(x) = \\underbrace{f(f(f(\\cdots f(x)))))\\}_{n\\text{ times}} \\) w... | D |
[
{
"content": "Determine which function is larger as $n$ becomes very large: $f(n)=2^{2^{2^n}}$ or $g(n)=256^{256^n}$.",
"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... | 13.45 |
[
{
"content": "Let $A \\in M_{10}(\\mathbb{R})$ be a real matrix that satisfies the equation $A^2 = A + 2I$. Given that the rank of $A + I$ is 3, find the trace of $A$. \\( \\text{tr}(A) \\).",
"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... | 5.37% |
[
{
"content": "A lattice point in the $x,y$-plane is a point both of whose coordinates are integers (not necessarily positive). How many lattice points lie on the graph of the equation $x^2-y^2=47$?",
"role": "user"
}
] | 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... | 0.46 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... | Trapp Co.
Schedule of Cash Collections of Accounts Receivable
| Month | One-third of Current Month's Credit Sales Collected | Two-thirds of Prior Month's Credit Sales Collected | Total Account Collections |
|---|---|---|---|
| August | $20,000 | $0 | $20,000 |
| September | $37,000 | $40,000 | $77,000 |
| October | $45,000 | $74,000 | $119,000 | |
[
{
"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... | monopolistic competition |
[
{
"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... | 6.7e-16 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... | 11.87% |
[
{
"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... | r/4 |
[
{
"content": "How many of the integers between 1 and 1000, inclusive, can be expressed as the difference of the squares of two nonnegative integers?",
"role": "user"
}
] | 750 |
[
{
"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... | 3.77s |
[
{
"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... | 130 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... | supine |
[
{
"content": "Does the statement \"$M_R$ is finitely generated and every submodule of $M_R$ is finitely generated\" imply that $M_R$ is a Noetherian module? Answer yes or no.",
"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... | $7,275.60 |
[
{
"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... | 625.4 MeV |
[
{
"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... | 1.4% |
[
{
"content": "Consider the polynomial \\( f(x) = x^7 - 4x^3 + x + 1 \\). Determine the number of roots of this polynomial that have a modulus less than 1 in the complex plane, taking into account the multiplicity of repeated roots.",
"role": "user"
}
] | 3 |
[
{
"content": "Consider a random walk on the complex plane starting at the origin, where each step is taken in the direction of a randomly chosen nth root of unity, and each step is of unit length. Let $X_N$ denote the distance from the origin after $N$ steps. Determine an upper bound for the expected value $E(X... | \sqrt{N} |
[
{
"content": "Evaluate the integral \\( \\int_{-\\pi}^\\pi \\left( \\sum_{n=1}^\\infty \\frac{\\cos(nx)}{2^n} \\right)^2 \\, dx \\).",
"role": "user"
}
] | \dfrac{\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... | 2e-5 V |
[
{
"content": "Evaluate the limit of the sequence \\((S_n)_{n \\in \\mathbb{N}}\\), where \\[S_{n}=\\frac{1}{\\ln(2n+1)}\\sum_{i=0}^{n}\\frac{((2i)!)^2}{2^{4i}(i!)^4}.\\] Determine the value of the limit as \\(n\\) approaches infinity.",
"role": "user"
}
] | \dfrac{1}{\pi} |
[
{
"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... | 7.8015 |
[
{
"content": "Does the uniform convergence of continuous functions $f_n$ to $f$ on $\\mathbb{C}$, where $f_n'$ does not exist, guarantee the existence of $f'$? Provide a justification for your answer.",
"role": "user"
}
] | No |
[
{
"content": "Find all pairs of natural numbers \\((x, y)\\) such that \\(x^3 - 3^y = 2015\\).",
"role": "user"
}
] | (14, 6) |
[
{
"content": "Let $\\mathfrak{g}$ be a complex reductive Lie algebra, and let $M$, $N$, and $L$ be finite-dimensional $\\mathfrak{g}$-modules. If $M$ is a quotient of $N$ and $N$ is a quotient of $L$, is $M$ necessarily a quotient of $L$?",
"role": "user"
}
] | Yes |
[
{
"content": "Let $V$ be a Banach space. Suppose $\\alpha_i$ is a collection of bounded linear functionals $V\\to \\mathbb{C}$ such that: $$ \\bigcap_i \\ker(\\alpha_i) = 0. $$ Does this imply that the $\\alpha_i$ span a dense subset of the dual $V'$?",
"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... | $6.32 million |
[
{
"content": "Let $a,$ $b,$ and $c$ be distinct complex numbers such that\n\\begin{align*}\na^3 &= 2a + 5, \\\\\nb^3 &= 2b + 5, \\\\\nc^3 &= 2c + 5.\n\\end{align*}Find $a^3 + b^3 + c^3.$",
"role": "user"
}
] | 15 |
[
{
"content": "Determine whether the function \\( g: \\mathbb{R}^3 \\to \\mathbb{R} \\) defined by\n\\[\ng(\\mathbf{y}) = \\dfrac{y_1y_2y_3}{y_1^2+y_2^4+y_3^2} \\quad \\text{if } \\mathbf{y} \\neq \\mathbf{0}\n\\]\n\\[g(\\mathbf{0}) = 0\\]\nhas a limit of 0 as \\( \\mathbf{y} \\to \\mathbf{0} \\).",
"role": ... | 0 |
[
{
"content": "Let $G$ be a finite group and $P$ a Sylow $p$-subgroup of $G$ contained in the center of $G$. Does there exist a normal subgroup $N$ of $G$ such that $P \\cap N = \\{e\\}$ and $PN = G$?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the minimum number of vertices $m$ such that the complete graph $K_n$ is a vertex minor of the path graph $P_m$. What is the value of $m$?",
"role": "user"
}
] | 2n - 1 |
[
{
"content": "Evaluate the line integral \\( \\int_C \\mathbf{F} \\cdot d\\mathbf{r} \\) where \\( C \\) is the curve joining the origin \\((0, 0, 0)\\) to the point \\((1, 2, 3)\\) defined by the parametric curve \\( \\mathbf{r}(t) = \\frac{\\ln t}{\\ln 2} \\mathbf{i} + t^{\\frac{3}{2}} \\mathbf{j} + t \\cos(\... | 21 |
[
{
"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... | 5.19% |
[
{
"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... | 4NH_3 + 3O_2 -> 2N_2 + 6H_2O |
[
{
"content": "Consider a connected complex manifold $X$ with a complex submanifold $Y$ such that a function $f:Y \\to \\mathbb{C}$ is holomorphic if and only if $f$ is constant. If $Y$ is not a closed submanifold, can $X$ have non-constant holomorphic functions?",
"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... | $16,000,000 |
[
{
"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... | {eq}h = \frac{k^2R}{1-k^2}{/eq} |
[
{
"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... | $3.22 |
[
{
"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... | 2.34 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... | 37.50% |
[
{
"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... | $2,073,839 |
[
{
"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... | 16.49% |
[
{
"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... | Bread Machines |
[
{
"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... | $2,395 |
[
{
"content": "Compute the limit as \\( n \\to \\infty \\) of the expression:\n\\[\n\\frac{1}{n}\\left(\\sin\\left(\\frac{2\\pi}{3n}\\right)+\\sin\\left(\\frac{4\\pi}{3n}\\right)+\\cdots+\\sin\\left(\\frac{(n-1)2\\pi}{3n}\\right)\\right)\n\\]",
"role": "user"
}
] | \dfrac{9}{4\pi} |
[
{
"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... | 0.0523 dL |
[
{
"content": "If $\\cos \\theta = \\frac{1}{3},$ find $\\cos 5 \\theta.$",
"role": "user"
}
] | \frac{241}{243} |
[
{
"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... | 3.59 A, enters the junction |
[
{
"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... | 62.93 km/h |
[
{
"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... | $40,076.03 |
[
{
"content": "Determine whether $R^n$ is projective as a module over $M_n(R)$. 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... | 104.29 N |
[
{
"content": "Determine the number of ways to arrange 10 fillér and 50 fillér coins in a straight line to cover exactly 1 meter, using at least 50 coins. The coins must be placed side by side, and the order of the two types of coins matters. The diameter of a 10 fillér coin is 19 mm, and the diameter of a 50 fi... | 270725 |
[
{
"content": "Evaluate the double integral \\(\\iint_{[0,1] \\times [0,1]} \\max\\{x,y\\} \\,{\\rm d}x\\,{\\rm d}y\\).",
"role": "user"
}
] | \dfrac{2}{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... | 11.714 |
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