Question: how to integrate on irregular area?

hello,my friends.I got a problem in using maple.

I want project a cuboid on a plane, and integrate function on that area.

for example, a cuboid which have a spatial diagonal between (0,0,0) and (1,2,1).
Then it was projected to a plane defined by three points (-1,0,0), (0,-1,0) and (0,0,-1).
Finally, a function x^2+y^2 was integrated on that projected area.

I found the cuboid can be defined with plottools:-cuboid and projected with plottools:-project in maple.
but how to integration next?
I can't find any commands in maple can do the integration with that irregular area.

I need some help.Thank you very much in advance.

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