So here's the way Mathematica sees it. 

Additional Requirements	Mathematica optional	*Maple required	*Matlab required
Hierarchical modeling that follows real-life topology
Multidomain modeling
Drag-and-drop model design
Work with Modelica models
Combine Modelica code with drag-and-drop design
Include external C functions
Biochemical pathways
Electrical (analog and multiphase)
Magnetic
Mechanical (translational, rotational, and 3D multibody)
Signal blocks (continuous, discrete, and logical)
State graphs
Thermal (heat transfer and fluid flow)
Hybrid continuous-discrete solver
Real-time solver
Sensitivity analysis solver
Initialize to steady state
One-click plotting of any system variable
Automatic 3D mechanical visualization
Custom visualization environment	Mathematica	Maple	Matlab
2D and 3D graphics language
Advanced 3D graphics (lighting, transparency, and more)
2D and 3D animation
Standard formats (.avi and .mov)
Instant interactivity
Analysis platform	Mathematica	Maple	Matlab
Programmable simulation control
Parallelized parameter sweeps
Model equation analysis
Model equilibrium detection
Control systems design
Model calibration
System optimization
Reusable standalone simulation executable
Interactive HTML model

Of course if Maple were to do a similar comparison on it's website it would probably include things Mathematica couldn't do.  A big difference is the fact that MapleSim cannot be used without Maple where-as System Modeller doesn't need to have Mathematica installed.

Awesome post by the way!

On M12 the image looks mosaic like
> restart; gc();
> with(ImageTools); with(plots); with(plottools);
> im := Read("c:/Program Files/Maple 12/data/tree.jpg");
> p := Preview(im);
> op(1, p):
> q := plot3d(1, x = 0 .. 2*Pi, y = 0 .. 2*Pi, coords = spherical, style = surface, grid = [235, 354]);
> display(PLOT3D(MESH(op([1, 1], q), op([1, 4 .. -1], p)), op(2 .. -1, q)), orientation = [-120, 30]);

I think there was a way to fix it but I couldn't remember.

Anyways, there are some world maps (cylindrical projection) someone has put together on the public domain here http://www.evl.uic.edu/pape/data/Earth/  linked from this page http://vterrain.org/Imagery/WholeEarth/

For me on M12 using the spherical option gives me that mosaic look, so I used coords=cylindrical just for display purposes, nothing fancy.  Here's the cylindrical look to my image

> restart; gc();
> with(ImageTools); with(plots); with(plottools);
> im := Read("c:/Documents and Settings/Cookie Monster/My Documents/Downloads/Topography.jpg");
> p := Preview(im);
> op(1, p);

> q := plot3d(1, x = 0 .. 2*Pi, y = 0 .. 2*Pi, coords = cylindrical, style = surface, grid = [177, 354]):

> display(PLOT3D(MESH(op([1, 1], q), op([1, 4 .. -1], p)), op(2 .. -1, q)), orientation = [30, 160]);

I would like to bridge this thread  http://www.mapleprimes.com/questions/130298-Jumble-Word-Permute

Because it is a major version.  Similarily you can't update (update is the word you intend) from Mathematica 7 to Mathematica 8. 

If you uploaded your code some experienced maple users could probably locate why it is freezing.

I suppose you mean when zooming a graph why does the text not shrink or increase?

I suppose you mean when zooming a graph why does the text not shrink or increase?

Whoa !!  No wonder no one posted an answer here.  It is a bit confusing. 

Anyone wishing to look further into this question (I decided to search and find and found)  can follow his work in length here
http://www.cheresources.com/invision/topic/14619-shell-and-tube-condenser-design/

There had been some considerable questioning and answering before he came here to mapleprimes and maple for some help.  It is, though, an interesting read.

I was actually fooled into thinking Samir Khan had come back to visit mapleprimes with a post (a celebration ensues over some interesting possible engineering marvels with maple that will come with his return) however, the celebration was extremely short lived when I saw it was unfotunately a post from the past. 

Just trying to figure out how one would type what YC has shown without the `*` in the entry line and getting it to show up in the answer.

Was able to type it out what he shows in his worksheet on Maple16 classic, document and worksheet mode and I was unable to replicate what YC has shown (all gave the answer of 1) except using his worksheet. 

He must have copy and pasted it from somewhere and Maple hid the `*` from view.  Curious as to the reasons why.

Just trying to figure out how one would type what YC has shown without the `*` in the entry line and getting it to show up in the answer.

Was able to type it out what he shows in his worksheet on Maple16 classic, document and worksheet mode and I was unable to replicate what YC has shown (all gave the answer of 1) except using his worksheet. 

He must have copy and pasted it from somewhere and Maple hid the `*` from view.  Curious as to the reasons why.

What do I get when I buy Maple 16?  Do I get hardcopy manuals?  Does a Maple 16 personal edition still exist?

@ Alejandro Jakubi - The above intended usage for dual worksheets is for comparison purposes.  Opening a new kernel and trying to open the already opened worksheet redirects me to the already opened worksheet.  I suppose I'll just save the same worksheet with two different names.

I still hear that Maple is not strong in numerics - however I find it very much adequate although others will probably disagree, and for that reason I pose a Maple 17 wish ... stronger numerics for Maple ... 

One can not measure the quality of a website accurately depending on the definition of quality being used.  The values obtained are objectionable especially if they are based on activity.  The word quality is also objectionable - quality as in content / layout or quality as in good connection, speed of information delivery etc...

I restarted and achieved the same result but if I do some other operation in the midst or just after restart the value changes slightly. 

For example, I first changed epsilon and sigma to rational values  epsilon:=convert(epsilon,rational) etc.. and of course I should observe a slight change  685.116351816730684 as you can see more decimal places have changed value. 

I also get different values if I simply restart; by itself or restart; gc():  different again if I went restart; with(plots):

Not really sure why adding with(plots) would affect the value.