Question: Integration over an implicit domain

Is there a way to tell Maple to compute an integral over a domain defined by an implicit condition?

A trivial example would be: integrate 1 over the 2D domain defined by x^2+y^2<=1.

I know it's possible to write the explicit double integral


Or even as a single integral:


However, it's not always possible to do this explicitly, depending on the form of the relation f(x,y)=0 defining the domain.


My idea was:


But Maple returns 0. However, evalf/Int returns the correct numerical value of Pi.


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