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Question: How to evaluate this integral?

Question:How to evaluate this integral?

Rouben Rostamian 8018 Maple 2021
integration piecewise discontinuous
June 25 2021
1

I need to calculate dozens of piecewise-defined  (but elementary) definite integrals of the following kind. Maple returns them unevaluated. Is there a trick to force evaluation? 

restart;
u := piecewise(0 <= x and 0 <= y and y <= x, x-1, 0 <= x and 0 <= y and x <= y, x, 0);
v := piecewise(0 <= x and 0 <= y and y <= x, x-1, y <= 0 and 0 <= x and -x <= y, x-1, 0);
plot3d(u*v, x=-1..1, y=-1..1);
# integrating over (0,1)x(0,1) works
int(u*v, x=0..1, y=0..1);
# but integrating over (-1,1)x(-1,1) returns unevaluated.
# How to force evaluation on (-1,1)x(-1,1)?
int(u*v, x=-1..1, y=-1..1);

integration-problem.mw

 
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