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I'am not sure but before this 6030 firmware update this examples were ok ?

laplace(f(t-a),t,s) => exp(-a.s).F(s) But with this firmware the cas on physical prime give the integral form...

And now if I try :

ilaplace(exp(-a.s).f(s),t,s) the result is : exp(-a.s)*f(s)*Dirac(t)

Any idea ?

Thank for comment.

Should be s,t instead of t,s for ilaplace.
I have never implemented something for laplace/ilaplace with a "symbolic" function (I mean something functional), only for fully defined expressions.