Question: Variables don't allow integration

I'm trying to calculate:

int(int((2-3*(x+y)+6*x*y)*(abs(x)^(2*H)+abs(y)^(2*H)+abs(x-y)^(2*H)), x = 0 .. 1), y = 0 .. 1);

where H is a number between 0 and 1 non-inclusive.

Maple seems not to be able to handle this even though it can calculate:

int(int((2-3*(x+y)+6*x*y)*(abs(x)^(2)+abs(y)^(2)+abs(x-y)^(2)), x = 0 .. 1), y = 0 .. 1);

I.e. without the H

Is there a way around this?

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