@Axel Vogt 

I see, well I'll just stick with the brute plotting then. It should work just fine. Thank you for all your help!

@Axel Vogt 

Yes, however, I had the adaptive=false flag in my plotting command for this very reason. What I am wondering, because it seems implied but it not explicitely stated. Is with adaptive=false if plot will always use just the number of points you specify with numpoints or if it may still choose to use more based on some other criteria.

For example:

If I use Kitonum's method and evaluate the 41 points I want prior to plotting then Maple is able evaluate almost instantly. However, if I try:

plot(Int(309.9615685*exp(3.936759889*phi-3.936759889*`ϕ`)*Heaviside(-phi+`ϕ`)*exp(-1549.807842*`ϕ`^2)/(Pi*sqrt(-15.74703956*phi+15.74703956*`ϕ`)), `ϕ` = -infinity .. infinity), phi = -1 .. 1, adaptive = false, numpoints = 41)

Trying to restrict the number of points again to 41 and plotting over the same interval Maple runs for many minutes and still does not return a result. 

@Kitonum 

Thanks! That does work very nicely for quickly generating the plot and is easy to do. Do you have any idea why just trying to plot the function would take so long even when telling Maple to restrict the number of plotting points? I guess it doesn't really matter if I can make the plot this way but I'm rather curious as to this behaviour. 

@ateaktree 

That link doesn't work either. Though it did when I previewed the draft. 

@Preben Alsholm 

Sorry, this is my first time doing this. I'll try the attachment once more and also include the plaintext of the integral.

The integral I am trying to plot is:

Int(R^2*exp((1/2)*(phi-`ϕ`)*sqrt(2)*R/sigma[sf])*Heaviside(-phi+`ϕ`)*exp(-(1/2)*`ϕ`^2*R^2/(R56^2*delta[un]^2))/(Pi*sigma[sf]*sqrt(-(2*phi-2*`ϕ`)*sqrt(2)*R/sigma[sf])*R56*delta[un]), `ϕ` = -infinity .. infinity)

with numerical values for constants:

Int(309.9615685*exp(3.936759889*phi-3.936759889*`ϕ`)*Heaviside(-phi+`ϕ`)*exp(-1549.807842*`ϕ`^2)/(Pi*sqrt(-15.74703956*phi+15.74703956*`ϕ`)), `ϕ` = -infinity .. infinity)

plotting.mw

@Axel Vogt 

Attached is the worksheet I am using.

plotting.mw