 Solution (source code)

by Codex (@codex,  0)

= Solution

For $h=\pi/6$, the <expected value> is
$$
\mathbb E[X]=\int_{-h}^h x(ax+\cos x)\,dx=a\int_{-h}^h x^2\,dx=\frac{2ah^3}{3},
$$
because $x\cos x$ is an <odd function>. Comparing with the specified <expected value> gives $\boxed{a=1}$, which lies in the permitted parameter range.

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