@Axel Vogt 

Yes you have right.Definition in Maple is:

F(w) = int(f(t)*exp(-I*w*t), t = -infinity .. infinity)

but in Mathematica is:

F(w) = *1/sqrt(2 Pi))*int(f(t)*exp(I*w*t), t = -infinity .. infinity)

@NaeemQau 

Add a numeric value for alpha ? and Then You have "too many boundary conditions: expected 22, got 23"?

Exit and Alt+F4 works as intended in Windows 10 Home build 1809 on Maple 2019.2.  

Do you have any reason to believe that a closed form symbolic(analytic) solution should exist? Questions like this should always indicate why it is reasonable to expect a solution. 

@johncarl 

int(1/(c*x + d)^2, x = a .. b) assuming a < b, 0 < a, 0 < c, 0 < d;

#-(-b + a)/((a*c + d)*(b*c + d))

int(y^2*exp(-I*omega*y), y = -infinity .. infinity);

#undefined

@Mohamed19 

Add a new Question   to MaplePrimes.It makes it convenient for them and more likely you will get someone to help you. 

Regards M.I.

Short answer: Mathematically is impossible,then Maple can't get rid of RootOf.

@ecterrab 

Hello

I have 7 examples that I have problem to calculate with precision 10 digits numerically.

See attached file:

InverseLaplaceTransform-numeric-Test.mw

Thanks.

@Toulousain 

It depends on the initial(boundary) condition and parameters,like :(r,p,b,s)

@ecterrab 

Yes, You'are right, my mistake.Thanks for explanation.

@nm 

 Notation %  is used with  packages "(MathematicalFunctions, Evalf)" to evaluate numericaly by  various methods like   Euler,Talbot.(Probably only work with inverse Laplace Transform).

@Jayaprakash J 

See answer Kitonum below.

https://www.mapleprimes.com/questions/200076-Slope-Of-A-Graph-At-A-Point

With No Maple:

https://math.stackexchange.com/questions/186752/proof-that-ex-is-a-transcendental-function-of-x