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$$f(x,y)=\int\limits_0^14\frac{x^2}{5}+2-y$$ \begin{gather}\tag{1} W_n (s) &:= \int_{[0, 1]^n} \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x} \end{gather} which occurs in the theory of uniform random walk integrals in the plane, where at each step a unit-step is taken in a random direction. As such, the integral (1) expresses the $s$-th moment of the distance to the origin after $n$ steps.