Question: Problem with integration involving Dirac delta function

We need to compute some integral, containing product of some "regular" function (e.g. gaussian)
and Dirac delta-function. The problem is that argument of delta-function is itself a function.

A simplified example is

d1:=s->int( g(x,5,0.025)*Dirac( s-f1(x) ) , x=0..infinity);

By trials and errors, we figured out that Maple runs such calculation successfully
when this function is very simple and fails in more complex cases, i.e., integration  returns zero.
In the simple example, we tried f1=1/x, and computation ran
successfully, but when we used the same as f2=sqrt( 1/(x^2) it returns
zero - as "evalf ( d1( 0.2 ) )"

In reality, we need this function (f1) to be something like

It seems that it is some internal limitation of Maple.
And we are wondering if there is a trick to overcome this limitation.

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