Question: "int" doesn't return a result in Maple 2018 but does in older versions


This more a warning to focus your attention on a specific point than a true question.

I submit you this test case which works in Maple 2015 and Maple 2016 but not in Maple 2018.

In a few words:

  • let X and Y two independant random variables with respective distributions Normal(mu__x, sigma__x) and  
    Normal(mu__y, sigma__y)
  • let Z := q -> cos(q)
  • You can easily verify that Maple can compute the formal expression of Mean(Z(X)) and Variance(Z(X))
    (which means that it could compute Z(X+Y) for X+Y is just another gaussian RV)
  • What I found is that:
    1. Mean(Z(X+Y)) returns same expressions in Maple 2015 and Maple 2016, but a different one in Maple 2018.
      Luckily the later is more readable than the former ones, and closer to the one of Mean(Z(U))  where U=X+Y is the RV of distribution Normal(mu__x+mu__y, sqrt(sigma__x^2+sigma__y^2))
      This suggest that the integration algorithm has evolved somewhere in between Maple 2016 and Maple 2018
    2. While Maple 2015 and Maple 2016 return an evaluated result for Variance(Z(X+Y)) Maple 2018 fails.

Can this "failure" be fixed by some adhoc option of Variance?
Or could it come from a "regression" in the implementation of this procedure (or of the underlying int procedure) in Maple 2018?

PS: I did not try to compute Variance(Z(X+Y)) from an explicit double integration

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