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... | Radiometric Dating |
[
{
"content": "Evaluate the total length of the curve \\( \\gamma: (0,2\\pi) \\to \\mathbb{R^2}, \\gamma(t)=\\bigg(t+\\sin(t), 1-\\cos(t)\\bigg) \\).",
"role": "user"
}
] | 8 |
[
{
"content": "If $\\frac{5}{33}$ is expressed in decimal form, what digit is in the 92nd place to the right of the decimal point?",
"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... | 1.52 kg |
[
{
"content": "Calculate the average value of the function \\( f(\\pi) = \\sum_{i=1}^7 |\\pi_i - i| \\) over all permutations \\( \\pi \\) of the numbers 1 to 7.",
"role": "user"
}
] | 16 |
[
{
"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... | 7712 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... | 7.5e-3 |
[
{
"content": "Evaluate the surface integral \\( \\int\\int_S z^2 \\, dS \\) over the triangle with vertices \\((1,0,0)\\), \\((0,2,0)\\), and \\((0,0,3)\\).",
"role": "user"
}
] | \dfrac{21}{4} |
[
{
"content": "Find all pairs of natural numbers \\(a\\) and \\(b\\) such that \\(\\gcd(a, b) = 1\\) and \\(\\frac{a}{b} = b.a\\), where \\(b.a\\) represents a decimal number. For example, \\(\\frac{5}{2} = 2.5\\).",
"role": "user"
}
] | (5, 2) |
[
{
"content": "Evaluate the infinite series: \\[ \\sum \\limits_{k=1}^{\\infty} \\frac{2k-1}{k\\cdot(k+1)\\cdot(k+2)} \\] Transform the series into a telescoping series and find its sum.",
"role": "user"
}
] | \dfrac{3}{4} |
[
{
"content": "Determine whether the following statement is true or false: A set $A$ is Lebesgue measurable if and only if for every $\\epsilon > 0$, there exist an open set $G$ and a closed set $H$ such that $H \\subseteq A \\subseteq G$ and $\\mu(G \\setminus H) < \\epsilon$. Provide a justification for your a... | True |
[
{
"content": "Let $a, b, c$ be positive real numbers. Find the minimum value of \\[ P = \\frac{a^2}{(a+b)^2} + \\frac{b^2}{(b+c)^2} + \\frac{c}{4a}. \\]",
"role": "user"
}
] | \dfrac{3}{4} |
[
{
"content": "Evaluate the limit: \\[ L = \\lim_{n \\to \\infty} \\frac{1}{n} \\cdot \\log\\left(3^{\\frac{n}{1}} + 3^{\\frac{n}{2}} + \\dots + 3^{\\frac{n}{n}}\\right). \\]",
"role": "user"
}
] | \log 3 |
[
{
"content": "Consider a function $f: [a, b] \\rightarrow [a, b]$ that maps an interval to an irrational number $r$, dividing it roughly into two equal parts. We assign a unique infinite bitstring to each rational number $q \\in \\mathbb{Q} \\cap [0, 1]$ based on whether $q$ is less than or greater than $f$ at ... | \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... | 250 g |
[
{
"content": "Given that \\( \\int_a^b g(x) \\, dx = 0 \\) for some function \\( g(x) \\) bounded by \\(-1 \\le g(x) \\le 1\\), find the minimum value of \\( \\int_a^b [g(x)]^2 \\, dx \\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine the degree of the minimal polynomial $m_{\\alpha}(x)$ for the element $\\alpha = \\beta^6$ in the Galois field $GF(2^4)$, where $GF(2^4)$ is constructed as $K[x]$ modulo $1 + x^3 + x^4$ and $\\beta$ is the class of $x$. The powers of $\\beta$ are given as follows:\n\n- $1000$ corresponds... | 4 |
[
{
"content": "Evaluate the value of the alternating series: $$\\sum_{n=0}^\\infty \\frac{(-1)^n}{2n+1}$$.",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Let \\(a, b, c,\\) and \\(d\\) be non-negative real numbers such that \\(a + b + c + d = 1\\). Determine the number of different ways to choose these numbers such that \\(a^2 + b^2 + c^2 + d^2 = \\max\\{a, b, c, d\\}\\).",
"role": "user"
}
] | 15 |
[
{
"content": "Compute the remainder of the power tower \\(2^{3^{4^{5^{6^{7}}}}} \\mod 9\\).",
"role": "user"
}
] | 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... | 19800 |
[
{
"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... | $2,531.91 |
[
{
"content": "Find a sufficient statistic for \\( \\theta \\) given the distribution \\( f_x(x) = \\frac{e^{-|x-\\theta|}}{2} \\).",
"role": "user"
}
] | (X_{(1)}, X_{(2)}, \ldots, X_{(n)}) |
[
{
"content": "Calculate the expected squared distance of the endpoint from the origin for a random walk consisting of n line segments, each of unit length.",
"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... | 100 g H2SO4 |
[
{
"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... | 0.7 |
[
{
"content": "Evaluate the limit \\( \\lim\\limits_{n\\to\\infty}\\frac{\\sum_{k=1}^n k^m}{n^{m+1}} \\) as \\( n \\) approaches infinity.",
"role": "user"
}
] | \dfrac{1}{m+1} |
[
{
"content": "Evaluate the limit: \\( \\lim_{x \\to 0} x \\left[ \\frac{1}{x} \\right] = 1 \\)",
"role": "user"
}
] | 1 |
[
{
"content": "Determine whether the following statement is true: If \\((f^{-1})'(x) = \\frac{1}{f'(f^{-1}(x))}\\), then does it follow that \\(f'(x) = \\frac{1}{(f^{-1})'(f(x))}\\)?",
"role": "user"
}
] | True |
[
{
"content": "Find the largest positive integer \\( n \\) such that the equation \\( \\lfloor \\log_2 1 \\rfloor + \\lfloor \\log_2 2 \\rfloor + \\lfloor \\log_2 3 \\rfloor + \\cdots + \\lfloor \\log_2 n \\rfloor = 1994 \\) holds.",
"role": "user"
}
] | 312 |
[
{
"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... | -$3,341,917 |
[
{
"content": "Compute the limit using the squeeze theorem and basic limit properties: \\[ \\lim_{n \\rightarrow \\infty} \\dfrac{\\tan\\left(\\dfrac{\\pi}{n}\\right)}{n\\sin^2\\left(\\dfrac{2}{n}\\right)} \\]",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Consider a sequence of complex numbers lying in a sector with an angular width less than \\( \\pi \\). If the sum of the real parts of the sequence converges for any two non-collinear directions in the sector, does the sum of the moduli of the sequence also converge? Answer 'yes' or 'no'.",
"r... | yes |
[
{
"content": "Determine if it is true that the binomial coefficient \\( {q+1 \\choose 2} \\) is semiprime if and only if \\( q = 3 \\), given that \\( q \\equiv 3 \\pmod{4} \\).",
"role": "user"
}
] | True |
[
{
"content": "Find the maximum value of $ab$ given that $a, b \\in \\mathbb{R}$ and satisfy the equations $a^2 + b^2 = 1 + \\frac{2ab}{a-b}$ and $\\sqrt{a-b} = a^2 + 5b$. What is the maximum value of $ab$?",
"role": "user"
}
] | 42 |
[
{
"content": "Calculate the Lebesgue integral of the function \\( f(x) \\) defined on the interval \\([0,1]\\) as follows: \\( f(x) = \\begin{cases} 0, & \\text{if } x \\in \\mathbb{Q} \\\\ x, & \\text{if } x \\notin \\mathbb{Q} \\end{cases} \\). Construct an increasing sequence of simple functions \\( \\{\\var... | \dfrac{1}{2} |
[
{
"content": "Evaluate the contour integral \\(\\oint_{\\Gamma}\\left(\\cos\\frac{1}{w}-\\cos^2\\frac{1}{w}\\right)dw\\) where \\(\\Gamma\\) is a circular contour of radius \\(r\\) centered at the origin, traversed in the counterclockwise direction.",
"role": "user"
}
] | 0 |
[
{
"content": "Let \\((X_n)_{n\\in \\mathbb{N}_+}\\) be a sequence of independent random variables such that \\(X_n \\sim \\text{Exp}(n)\\). Define \\(Y_n := \\frac{1}{n} \\sum_{i=1}^{n} X_i\\) for \\(n \\in \\mathbb{N}_+\\). Does the sequence \\((Y_n)\\) converge in probability?",
"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... | Stock buy-back, distributing dividends to shareholders, increasing the amount of earnings per share, and mergers and acquisitions |
[
{
"content": "Calculate the integral: \\[ \\int_{0}^{\\frac{\\pi}{2}} \\frac{\\sqrt{\\sin x}}{\\sqrt{\\sin x} + \\sqrt{\\cos x}} \\, dx \\]",
"role": "user"
}
] | \dfrac{\pi}{4} |
[
{
"content": "Given a ring \\( R \\) and an ideal \\( \\mathbf{a} \\), let \\( \\pi: R \\rightarrow R/\\mathbf{a} \\) be the natural projection map. Define \\( \\pi^*:\\mathrm{Spec}(R / \\mathbf{a}) \\rightarrow \\mathrm{Spec}(R) \\) as the pullback of \\( \\pi \\). Determine the image of \\( \\pi^* \\) in \\( ... | V(\mathbf{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... | 3.12e6 |
[
{
"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... | 4.9% |
[
{
"content": "Evaluate the integral \\( \\int_0^{2\\pi} \\cos(\\cos(z))\\cosh(\\sin(z)) \\, dz \\) using a corollary of Cauchy's Integral Formula.",
"role": "user"
}
] | 2\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... | 9.33 |
[
{
"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... | 4.87e-5 |
[
{
"content": "Does a countable product of topological spaces, each having a countable basis, have a countable basis?",
"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... | 9.32% |
[
{
"content": "How many odd integers are there between $\\frac{17}{4}$ and $\\frac{35}{2}?$",
"role": "user"
}
] | 7 |
[
{
"content": "Given a right circular cone with an isosceles right triangle as its axial cross-section, where \\( P \\) is the vertex, \\( PA \\) is a generatrix, and \\( B \\) is a point on the base, find the maximum value of \\( \\frac{PA + AB}{PB} \\).",
"role": "user"
}
] | \sqrt{4 + 2\sqrt{2}} |
[
{
"content": "Compute \\(4^{22222} \\mod 121\\).",
"role": "user"
}
] | 16 |
[
{
"content": "Given real vector spaces $X$ and $Y$, consider the canonical bilinear map $X \\times Y \\rightarrow X \\otimes Y$ defined by $(x, y) \\mapsto x \\otimes y$. If $x \\in X$ is non-zero, is the induced linear map $y \\mapsto x \\otimes y$ injective? Justify your answer using the universal property of... | 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... | $2,646,000 |
[
{
"content": "Twenty people, consisting of 10 couples, are randomly seated at 5 tables with 4 seats each. What is the expected number of couples that sit together at the same table?",
"role": "user"
}
] | \dfrac{30}{19} |
[
{
"content": "Determine whether there is a real solution to the differential equation \\( \\frac{d^4y}{dx^4} = -y \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Given the linear regression model with the design matrix \\(X = [x_1 \\mid x_2 \\mid \\cdots\\mid x_p] \\in\\mathbb R^{n\\times p}\\), where the columns of \\(X\\) are centered (i.e., \\(x^T_j 1_n = 0\\) for \\(j = 1, \\ldots , p\\)), and the model does not include an intercept, assume the followi... | \dfrac{1}{10} |
[
{
"content": "Consider a continuous function $f: [-1,1] \\rightarrow \\mathbb{R}$ such that $f(-1)f(1)<0$ and $f''(x) < 0$ for all $x \\in (-1,1)$. Does the Intermediate Value Theorem guarantee the existence of a point $x \\in (-1,1)$ such that $f'(x) = 0$?",
"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... | Reproductive Isolation |
[
{
"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... | f1 = 7.27 Hz, f2 = 14.5 Hz, f3 = 21.8 Hz |
[
{
"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 m |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n \\to \\infty} \\left(\\frac{(n+1)(n+2)\\dots(3n)}{n^{2n}}\\right)^{\\frac{1}{n}} \\]",
"role": "user"
}
] | \dfrac{27}{e^2} |
[
{
"content": "Consider a group $G$ of order $105$. Determine the number of Sylow 3-subgroups of $G$.",
"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... | 1.70 x 10^3 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... | Dec. 3
Merchandise 28,500
Accounts payable 28,500
Prepaid freight 900
Cash 900
Dec. 5
Merchandise 18,750
Accounts payable 18,750
Dec. 6
Accounts receivable 17,550
Sales 17,550
Cost of merchandise sold 14,000
Merchandise 14,000
Dec. 7
Accounts payable 3,000
Merchandise 3,000
Dec. 13
Accounts payable 28,500
Cash 27,930
M... |
[
{
"content": "Evaluate the limit: $$\\lim_{x \\to \\infty} \\left[\\left(\\frac{(x+1)!}{e^{x+1}}\\right)^{\\frac{1}{1+x}} - \\left(\\frac{x!}{e^x}\\right)^{\\frac{1}{x}}\\right].$$",
"role": "user"
}
] | \dfrac{1}{e^2} |
[
{
"content": "For the function \\( G(x) = x \\cos(x^M) \\), where \\( M \\) is a natural number, determine the smallest positive integer \\( k \\) such that \\( G^{(k)}(0) \\neq 0 \\).",
"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... | 19.60 |
[
{
"content": "Does every IA automorphism \\( \\varphi \\in \\mathrm{IA}_n \\) have a fixed point in the complement of the commutator subgroup \\( [F_n,F_n] \\)?",
"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... | 1.0e+2 m/s |
[
{
"content": "Find an upper bound for the operator norm \\( \\lvert e^A \\rvert \\) of a square matrix \\( A \\) in terms of \\( \\lvert A \\rvert \\) and the dimension \\( n \\) of the matrix.",
"role": "user"
}
] | e^{\lvert A \rvert} |
[
{
"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... | n = 5, l = 0, m_l = 0, s = +1/2 |
[
{
"content": "Can the second person ensure that a 60-digit number, written alternately with the first person using only the digits 1, 2, 3, 4, and 5, is divisible by 9 if the first person tries to prevent it?",
"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... | 2939.1 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... | 109.5 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... | 1662.5 rev |
[
{
"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... | 1.4e+2 L |
[
{
"content": "Determine the total number of real solutions to the equation \\(x^2 = 2^{-x}\\).",
"role": "user"
}
] | 3 |
[
{
"content": "Find the average value of the function $x^2$ over a circle of radius $1$ using integral calculus.",
"role": "user"
}
] | \dfrac{1}{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... | 1,118.744 per unit |
[
{
"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... | 1/10000000 |
[
{
"content": "Determine the isomorphism class of the quotient group \\( \\mathbb{Z}^2 / \\langle (5, 3) \\rangle \\).",
"role": "user"
}
] | \mathbb{Z} |
[
{
"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... | 26.24 N |
[
{
"content": "Given the cumulative distribution function (CDF) of a random variable X:\n\n\\[ F(x) = \\begin{cases} 0, & \\text{if } x < 0 \\\\ \\frac{1}{4}, & \\text{if } 0 \\le x < 1 \\\\ \\frac{2}{5}, & \\text{if } 1 \\le x < 2 \\\\ \\frac{2x-3}{2}, & \\text{if } 2 \\le x < 2.5 \\\\ 1, & \\text{if } x \\ge 2... | \dfrac{59}{40} |
[
{
"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... | 65.354 mmol/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... | 30 N |
[
{
"content": "For what positive value of \\(c\\) does the equation \\(\\log x = cx^4\\) have exactly one real solution for \\(x\\)?\n\\(\\text{(A) } \\frac{1}{4e} \\quad \\text{(B) } \\frac{1}{4e^4} \\quad \\text{(C) } \\frac{e^4}{4} \\quad \\text{(D) } \\frac{4}{e^{1/4}} \\quad \\text{(E) } 4e^{1/4}\\)",
"... | 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... | 68.86 |
[
{
"content": "Determine whether there exist integer functions $f(n)$ and $g(n)$ such that \\( \\lim_{n \\to \\infty} f(n)\\zeta(2) + g(n) = 0 \\) and \\( f(n)\\zeta(2) + g(n) \\neq 0 \\) for all positive integers $n$, where \\( \\zeta(2) = \\frac{\\pi^2}{6} \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the integral \\( \\int_{0}^{1}\\frac{\\arctan(x)}{x}dx \\) and compare your result with Catalan's constant, \\( K \\).",
"role": "user"
}
] | 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... | Kc=[HCO3-][OH-]/[CO32-] |
[
{
"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... | 4.813 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... | 15.14% |
[
{
"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... | 8.3e-4 T |
[
{
"content": "In \\(\\triangle ABC\\), \\(\\angle{ABC} = 90^{\\circ}\\). Points \\(P\\) and \\(Q\\) are on \\(BC\\) and \\(AB\\), respectively, such that \\(\\angle{BAP} = 7^{\\circ}\\), \\(\\angle{CAP} = 14^{\\circ}\\), and \\(\\angle{BCQ} = 23^{\\circ}\\). Given that \\(AB = AC \\cdot \\cos (\\angle{BAC})\\),... | 30^\circ |
[
{
"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... | 136.5 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... | 248 |
[
{
"content": "Evaluate the infinite product \\( \\prod _{n=2}^\\infty \\left(1+ \\frac{1}{n^2}+\\frac{1}{n^4}+\\frac{1}{n^6}+\\cdots \\right) \\).",
"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... | 10.06% |
[
{
"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... | $93,770.12 |
[
{
"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... | Forward Rate = Spot Rate * ((1+ Foreign Rate)^(Days/365) / (1+ Domestic Rate)^(Days/365)) |
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