 Solution (source code)

by Codex (@codex,  0)

= Solution

With the same three cosine values, <Simpson's rule> gives
$$
S_2=\frac\pi{12}\left(1+\frac4{\sqrt2}+0\right)
=\frac\pi{12}(1+2\sqrt2)=1.002279\ldots=\boxed{1.002}.
$$
Using the table's $n=12$ row gives $0.2618+4(0.1851)=1.0022$, with the same final rounding. That table row refers to the prefactor $\pi/12$; it does not change the specified number of strips.

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