Here is one way to do this without using the "sphere" command.

restart: with(plots):

animate( implicitplot3d, [x^2+y^2+z^2=A, x=-2..2, y=-2..2, z=-2..2], A=1..4 );

You can substitute your own equation for the above.  Look into the animate and the implicitplot3d commands for more details.  

Another way using rational values similar to what was done above in previous replies.

Download 221_solutions_lost.mws

The Maplesoft applications center has an example.  Here is the link.  The worksheet below is a modified version of the example from the link to make it look like the equation that you supplied.  The initial conditions are the ones from the example.

Download 221_vander.mws

Use dsolve with your initial conditions, and then vary the variable "k" before plotting. Below, this is done inside of the plot command. 

restart: with(plots):

de:=4*diff(x(t),t,t)+3*diff(x(t),t)+k*x(t)=0;

ic:=x(0)=0,D(x)(0)= 1:

p:=dsolve({de,ic},x(t));

X:=unapply(rhs(p),t):

pp:=seq(plot(X(t),t=0..20),k=1..6):

display(pp);

If you want to see the plot for only one value, limit the range variable k= so that the ending value is the same as the beginning value.  

Your V range is between 1132.2 and 1383.8.  Rewrite your equation and use fsolve, with a starting value of 1200.  See the help pages for fsolve for more details on this.

restart:

eq:=(40=53802.8616296/V-4421522.681759509154376431238971030890884/V^2-34696412.12593013477367899170424836286055/V^3-68770455564.45999796126160810938763183857/V^4+403332559275.4141930212434442368214769780/V^5+958128028485.0130104382506076504882209562/V^6-26140204752481.13476652750626233649550628/V^7+17375263330.60863159106251286006887257238*ln(V)/V^4);

fsolve(eq,V=1200);

ans:=%;

eval(eq,V=ans);

 

?DiscreteTransforms[FourierTransform] will take you to the help page.  Look at the examples for real 2D data.  In order to use the commands, you must load the package first, as shown in the first example.

Start here, and try some of the examples in the file that you download, by changing the functions to match your own.  See what happens.   The following YouTube tutorial is useful as well.

Here is one way.

> restart:with(LinearAlgebra):
> test:=Matrix([[1,2,3],[4,5,6],[9,8,7]]);
> rr:=(Row(test,-2));
> add( i, i=rr );
> rs:=(Row(test,-1));
> add( i, i=rs );
> rp:=(Column(test,-1));
> add( i, i=rp );
 

Download 221_MatrixRowColumnAdd.mws

See the help files for the VectorCalculus package.  This link has a  worksheet from the Maple Applications Center that covers most of the commands, and it deals with coordinate transformations and well as examples of velocity and acceleration derived from position.

Once you fix the last multiplication from e^(-R^2) = 0 to exp(-R^2), you end up with one (1) equation with three (3) unknowns.  So, what exactly are you looking for?  Each variable solved with respect to all of the others, one by one?  Do you have values for R, theta, phi?

Download 221_separation.mws

Here is an example taken from the help pages for the "animate" command. It is used together with "textplot" and "display".  I might be misinterpreting what you are looking for.

restart:  with(plots):

a:=animate( plot, [A*(x^2-1),x=-4..4,color=blue], A=-2..2):
b:=animate( plot, [(x-A)^2-1,x=-4..4], A=-2..2 ):
c:=textplot([3,10,`A*(x^2-1)`],align={ABOVE,RIGHT}):
d:=textplot([3,6,`(x-A)^2-1`],align={ABOVE,RIGHT}):

display(a,b,c,d);

 restart:

eqn:=s^5+3.236067976*s^4...

evalc(eqn);    #This will seperate the equation into Real and Imaginary parts

evalc(Re(eqn));  #This will return only the real part of the equation

If pdsolve is being used, then ?pdsolve/numeric/errorcontrol would be the place to start.  As with dsolve/numeric, this help page has examples as well that illustrate the tradeoffs between solution "resolution " and time. 

Download 221_pdsolve_timestep.mws

The Maple help command for the differential equation solver has a good description for all of the methods available to it, with a variety of options.  It is a good starting point for you question.

?dsolve[Error_Control]

will bring up the help page.

At a very high level, more steps=higher accuracy, BUT this depends on the type of problem you are solving.  For fixed step algorithms, a large step is used for signals that vary slowly and small steps for signals that vary quickly.  So, if you have a fast varying signal, you will need a finer resolution in your step size, which will increase the accuracy of your result (as well as the time it takes to compute it).

I did not try the first worksheet that you mentioned, and I was hasty with my reply this morning.  I am experiencing the same problem, but I can generate the plots just by cutting and pasting the output of the functions.

For example, DegreePlot(1); will just spit out the display command followed  by ([    pieslice([0, 0], 1, 0......  if you cut and paste everything including the display command and execute this in a new worksheet (you have to use with(plots) and with(plottools)), it seems to work.

I unzipped all of the files in this directory on my WinXP machine:

c:\temp\Maple\Trigonometry

Using the first worksheet as an example, I modified the path name to look like this:

libname:="C:\\temp\\Maple\\Trigonometry\\", libname:

Then using the following command I got a listing of the functions that are in the library file:

march('list', "maple.lib");

Then you can see what each of the function calls do by using the showstat command.  For example:

showstat(SolidPlotRCol);

SolidPlotRCol := proc(f, a, b)
local c;
   1   c := COLOR(RGB,5*evalf(1/10000000000000*rand(),2),5*evalf(1/10000000000000*rand(),2),5*evalf(1/10000000000000*rand(),2));
   2   plot(f(x),x = a .. b,filled = true,color = c,style = patchnogrid)
end proc
 

Hope this helps.