This paper uses the mathematical software Maple as the auxiliary tool to study the evaluation of two types of double integrals. We can find the closed forms of these two types of double integrals by using Euler's formula and finite geometric series. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem- solving methods.
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