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.

@William Simpson The GUI is the interface that should initially start by default when you load Maple.

Typing in libname; and executing will give you the path location to lib on your hard drive.  Then you can place the files required in that location to run direct search optimization application.   Or follow the other instructions Acer gave you. 

@MortenZdk Yes the RandomVariable call has to be made otherwise, as you found out, it doesn't work.

@JonMcLoone I think Maplesim follows that same pricing model you describe.  For MapleSim I was kind of surprised to see second digit releases were not actually partial upgrades but full blown releases. 

For Maple, at least currently, all sub releases first and second digit releases are free updates, while third digit or letter releases seem to be reserved for fixes that require immediate attention. 

It's nice to see new features in a free update - it helps retain users.  IN the past only two categories existed - Major releases and minor updates or patches.  Nowadays it's looking more and more like four - Major releases - Minor releases - Major updates and Minor updates. 

It scares me when companies change their pricing models because it usually means paying a little more.  It's a heavy model to weigh, push and pull, customers and company, higher cost for more features and customer satisfaction or lower cost and less features with similar customer results or no change in cost with added features and very high customer satisfaction. 

Creating such a pricing model could be done quite easily and cheaply in Mathematica or Maple.  I wonder if Mathematica uses Mathematica to discover such things?

Are versions 10.1, 10.2, 10.3, and 10.4 free updates for 10.0?

@DSkoog Didn't you forget something important in the graphic?

@Carl Love Actually 2 applications for FEM applications prior to Maple 10 come up.  Finite element methods for solving PDEs  and  Finite Elements Package.  I'm not sure wether these would be of any use.

It would be nice to see some imrpovement in Maple in the FEM and FEA area, it would hit at some of the strengths that exist in Matlab or Cosmos.  I am sure Samir Khan wouldn't hesitate to agree with that. 

As Carl hinted, there is some great opportunities to extend Maples features here, either by a third party or from Maplesoft itself. 

You could upload your code here and certainly someone could help.

@roman_pearce I'm confused about support. 

As far as I'm concerned Maplesoft supports only the current release.  I don't recall ever seeing the release of a bug fix prior to the current version. 

Now if by support you mean a help line, then ok that makes perfect sense.  I think I just texted myself into the answer.