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How to fix Runtime Error while doing integration?

I'm trying to evaluate:


where z is:

z = 1-exp(2.0*cos(t) - 2.0*sin(t)-0.4*sqrt(-25*(cos(t) - sin(t))^2 + 100)^2)

But it is throwing following error:

RuntimeError: ECL says: THROW: The catch RAT-ERR is undefined.

I' new to Sage, but following through some posts at ask.sagemath (I can't post link), I feel it may be due to precision. 5 digits are OK with me.

Any fix/workaround? Thanks.