@Carl Love Won't be able to get to Maple till morning.  I wonder if sockets would be a better option.

@acer What I meant was point has to be called.  Distance won't work without some call to point

@one man I just mentioned I created one at 19kb, much smaller than the one you made and it didn't work.  So I was thinking it was probably Maples GIF format.

Actually I got it down to 19kb and it doesn't work.  It must be the formatting of the gif file that Maple exports that is different than a standard animated GIF file that prevents it from working.

@one man It's too bad it can't be done completely within Maple.

I've tried from Maple and I can't get anything exported out of Maple in animated GIF to work. 

Decreased frames to 3, turned off anti-aliasing and I can get a simple file down to 39kb but either that's too big or Maple exports animated GIFs in some strange format that doesn't work on the Mapleprimes website, maybe it doesn't work on other websites I don't know. 

almost as if when the converging lines sqrt(x^2+y^2)-sqrt((x-4)^2+(y-3)^2) = 3  ... 4 ...4.5  etc... cross over one another they blank each other out.

adding numpoints=50000 defines the line until it collides again "blanking it out"

Increasing the range to 2e15 produces some interesting results and adding numpoints=500000

As a note you will have to execute the libname command each session if you wish to use commands from the DirectSearch library.

To have them automatically loaded, not to add complexity to your situation, open notepad and type in the line

libname:= "****",libname  -- where inside quotes replace **** with the location of your new .hdb and .mla files.  The ,libname just means to include your system library.

saveas (the notepad file) as maple.ini in your Maple2016 directory.  This way every time Maple is started it will automatically include the new DirectSearch commands.

@William Simpson You could add files to the original Maple installed directory (the first variant) - however you may have heard, which is probably cause for your concern, that it is generally a bad idea to install libraries in the system library.  Some people do that.   Others prefer to create a seperate directory (the safer second variant) to differentiate between original installed library files and add-on library files and possibly avoid conflicts that might arise.

It seems difficult if you've never done it before, but after that it will be a piece of cake.

The DirectSearch2.zip archive contains:
  examples.mw      – examples of package usage,
  DirectSearch.mla – Package Archive File,
  DirectSearch.hdb – Package Help file,
  CDOS method.pdf  - CDOS method description.

Package installation instruction.

The first variant.
    1. Find the directory where your Maple installed.
    2. Find the subdirectory \lib\
    3. Copy the following two files into this subdirectory:
        DirectSearch.mla,
        DirectSearch.hdb.

The second variant.
    1. Create the directory, for example, C:\DirectSearchLib\
    2. Copy the following two files into this directory:
        DirectSearch.mla,
        DirectSearch.hdb.
    3. In current Maple session execute the command:
        > libname:=”C:\\DirectSearchLib”, libname;

Wouldn't it be easier to use plottools:-translate?

Looking at the help page of https://reference.wolfram.com/language/ref/NormalDistribution.html The shading is different in the two softwares. 

I produced the same plot in Maple 

with(Statistics):
plot([seq((unapply(PDF(RandomVariable(Normal(0, i)), t), t))(t), i = [.75, 1, 2])], t = -6 .. 6, color = [blue, orange, green], filled = [[color = blue], [color = orange], [color = green], transparency = .7])

plot([seq((unapply(PDF(RandomVariable(Normal(i, 1.5)), t), t))(t), i = [-1, 1, 2])], t = -6 .. 6, color = [blue, orange, green], filled = [[color = blue], [color = orange], [color = green], transparency = .7])

Download distribution_mathematica_in_maple.mw

@Carl Love indeed I copied your code over to a new sheet and executed with(Statistics) but forgot to include assigning X.  No problems then

Thanks for the codes.

@Carl Love 

I get an error using your code:
Error, invalid input: FillPlot expects its 1st argument, P, to be of type specfunc(PLOT), but received DensityPlot(X)

I was using the filled option wrong.

The value of the filled option can also be a list containing one or more suboptions (color, style or transparency).  The options in the list are applied only to the filled area, and not to the original curve itself.

So that applies to the filled=list option.  Adjusting Kitonums answer

plot(f(t), t = -5 .. 5, color=blue,filled=[color = blue, transparency=.9]);

@William Simpson That's the directory location of where you put your .mla and .hdb files in the zip file you downloaded from the application that was referenced to you. 

There is a readme.txt file in the zip file you downloaded, there are instructions for you in there as well. 

After placing those two files from the .zip file executing with(DirectSearch) will allow you to use those commands you want to use.

@William Simpson ok, I think I might see the issue here.

When you click on Maple to start it it opens a start page.  You can either go File menu pick New and then choose Document mode.  Or just click click on the New Document icon on the top left.  From there you will go into a blank new document sheet where you can enter commands. 

From there enter libname;

Tell us if you can get to that point and we'll go from here.

@Carl Love thanks for the inputs.  This answers what I was looking for.

Regarding using an option transparency for the filled=true in Kitonum's answer in the help page it says it doesn't affect the original curve.  But when you adjust the transparency it actually does - I think I interpretted that correctly.