One can also use scipy (faster) or mpmath (very slow)

sage: import scipy.integrate
sage: scipy.integrate.dblquad(lambda x,y:abs(cos(x+y)),0,pi,lambda x:
0,lambda x:pi)
(6.2831850310568189, 8.0696816340264377e-08)
sage: n(2*pi)
6.28318530717959

sage: from mpmath import *
sage:  mp.dps = 50; mp.pretty = True
sage: f=lambda x,y:abs(cos(x+y))
sage: quad(f,[0,pi],[0,pi],error=True)
(6.2831855317509475219920730867134288376181856252723, 0.000001)

Andrzej Chrzeszczyk

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