Given a function:
$$ F(k) = \sum_{k=600}^{999} \left(\left(\pi^2 \right(\frac{k}{1000} + x - 1\left)^2 \right)^{10^{-7}}\right)$$ where $0.1<x<0.35$.
The remainder term of the Euler Maclaurin sum of such function, where $p = 4$ and is given by;
$$\int_{599}^{999} \frac{\left(B_4(k - \lfloor k \rfloor\right)}{4!} \left(\frac{d^4k}{dk^4} \left(\pi^2 (\frac{k}{1000} + x - 1)^2\right)^{10^{-7}}\right) dk $$
How do I go about calculating such integrals?