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Answers
$f(x, y)=x^{4}+2 x^{2} y^{2}+y^{4}$ where
$$D=\left\{(r, \theta) | 3 \leq r \leq 4, \frac{\pi}{3} \leq \theta \leq \frac{2 \pi}{3}\right\}$$
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