Take a look at the help pages for the kernelopts command.

>?kernelopts

I don't know if I got it right, but here is my attempt at your problem.

View 221_trussbuckling_gk.mw on MapleNet or Download 221_trussbuckling_gk.mw
View file details 

I was wondering why fsolve could not handle the above polynomial.  It was an error on my part.  I was hasty in my respone.  fsolve with the "complex" option returns an answer. 

Acers version above is a better solution to the original question.

>fsolve(t^6+t^3+1,t,complex);

-.9396926208-.3420201433*I, -.9396926208+.3420201433*I, .1736481777-.9848077530*I, .1736481777+.9848077530*I, .7660444431-.6427876097*I, .7660444431+.6427876097*I

The commmands in Maple for extracting roots of a polynomial 
with respect to one variable are:

roots and Isolate

For more help on these commands:

?roots

?Isolate

?fsolve

You can also use the fsolve command to give you a 
numerical solution.  For your particular example, 
none of the above methods seem to work in Maple.

>restart:

>with(RootFinding):
>f:=t^6+t^3+1; Isolate(f);

>roots(t^6+t^3+1,t);

>fsolve(t^6+t^3+1=0);

P.S. How did you solve this by hand?

Regards,
Georgios Kokovidis

>with(plots):

>a := plot(sin(x)^2-cos(x)^2,x=0..2*Pi,coords=polar,thickness=3,color=green):
>b := coordplot(polar,labelling=true):
>display([a,b]);

>Grid:= seq(plot(j,theta=0..2*Pi,coords=polar,colour=gray),j=1..5),
seq(plot([r,Pi*j/6,r=0..5], coords=polar, colour=gray), j=0..11),
seq(textplot([j,-0.3,j]), j=1..5),
seq(textplot([5.5, Pi*j/6, j*30], coords=polar), j=0..11):

display([ a, Grid], axes  = none);

Start by looking at the help pages for DEplot.

>?DEtools[phaseportrait]

The example is from the help pages, with animation added.  The extra line at the end (animatecurves=true), is responsible for this.  Righ click on the plot, go to Animation, and then Play.  Substitute your equation for the equation below.

>restart: with(DEtools):
>phaseportrait(D(y)(x)=-y(x)-x^2,y(x),x=-1..2.5,[[y(0)=0],[y(0)=1],[y(0)=-1]],title=`Asymptotic solution`,colour=magenta,linecolor=[gold,yellow,wheat],animatecurves=true);
 

Another way to do this, in order to see if your equation is typed in correctly is as follows.

>restart: with(DEtools):
>eqn:=D(y)(x)=-y(x)-x^2,y(x);

>phaseportrait(eqn,x=-1..2.5,[[y(0)=0],[y(0)=1],[y(0)=-1]],title=`Asymptotic solution`,colour=magenta,linecolor=[gold,yellow,wheat],animatecurves=true);

Post the actual equations.  It sounds like C is an arbitrary constant, either as a multiplying factor to f(x) or to g(x), or it is the constant  of integration , which  is  assumed  after integrating  f(x)  or g(x).  Knowing which of the two C  options above that  C belongs  to might help.  Assuming the latter, are you looking for the value of C (a constant of integration) that holds for your  statement of the areas between the two functions being "mimimal"?

Take a look at the help pages for DEplot.  The option for number of frames is responsible for controlling the speed.  The example in the help pages has numframes=100.  Changing this number increases or decreases the speed.

animatecurves creates an animation of the evolving solution curve from the specified initial value(s) with respect to time. The default number of animation frames is 25, which can be changed with the numframes option. dsolve[numeric] is used to compute the solution curves for all specified initial values at different times. Note that if numpoints is provided, and the number of intervals (numpoints-1) does not divide evenly by the number of frame intervals (numframes-1), then a warning is produced, and numpoints is modified to be ceil((numpoints-1)/(numframes-1))*(numframes-1)+1.
 

>restart:with(DEtools):

>vdP := [diff(x(t),t)=10*(y(t)-x(t)^3/3+x(t)),diff(y(t),t)=-1/10*x(t)];
>DEplot(vdP,[x(t),y(t)],t=0..20,x=-2..2,y=-1..1,
title=`van der Pol oscillator`,dirfield=[[0.2,0.2],[-0.2,-0.2]],
arrows=comet,color=blue,animatefield=true,numframes=500);

Regards,
Georgios Kokovidis

Dräger Medical

Take a look at the "Line" command, that is part of the Student package.  ?Line for more help on this.  An example below, although I am not sure that this is what you are trying to do.  There are other ways to do this, the example highlights some of the built in tools.

>restart: with(Student[Precalculus]):

>for i from 1 by 1 to 4 do  Line([4,5], i, output=plot)  end do;

or

>restart: with(plots):

>animate((5+x*t), x = 0..10, t = 0..3,  frames =10);

Right click on the plot, Animation->Play
 

Regards,
Georgios Kokovidis

Dräger Medical

Good work Axel.  I struggled with this one for a while.  I was perplexed by the original posters "working" equation. 

-7e05+2.7e06*exp(((z-656.1)/9)^2)

This gives me an empty plot.  I am curious as to how this equation came to be, given the original data.  For a "gaussian" fit, given an exponential function, is seems that the Levenberg-Marquardt algorithm (LMA) might more suited to handling this type of data.  There is a case study in "Applied Maple for Engineers and Scientists" by Chris Tocci and Steve Adams, Chapter 3, that deals with this type of problem.

P. S.  I uploaded your file again below. 

Download 221_some_pdf_fitting.mws
View file details

The steps outlined below are for my PC using Maple 11 on a Win XP machine.

I unzipped the Gravitation package into my temp directory.  The full path is:

C:\temp\Maple\Gravitation

In that directory there are 4 files.  maple.ind,maple.lib,Docementation.mw and Gravitation.mw

The line below is what I have in my maple.ini file located in the Maple11\Users directory.  By default, this file does not exist.  You have to create it and save it using a text editor.  I used notepad to do this.  Open a blank document, and cut and paste the line below into this file.  Then save it as maple.ini

libname := libname, `c:/temp/Maple/Gravitation`:

Before saving the above line in your file named maple.ini, make sure that your path is representitive.  Modify the line above to match the location of the 4 files that you unzipped.  Make sure Maple is not running when you do this.  Maple looks for this file on start up.  Once the ini file is saved, double click the Documentation.mw worksheet.  This will start Maple and load the worksheet.  If everything went o.k. up to this point, then the worksheet will execute without any errors.  I tried this using the steps above and it worked.

 > restart:
> with(DEtools):
> with(plots):
> F:=DEplot(D(x)(t)=(x(t)/t),x(t),t=-0.1..0.1,x=-1..1):
> C:=contourplot((x(t)/t),t=-0.3..0.3,x=-1..1,color=blue):
> display(C,F);
 

>restart: with(Student[Calculus1]):
>Asymptotes((6*x^2)/(x^3+2*x^2-5*x), x);
 

I am using Maple 11 classic interface.  

A more compact way to do this.

>restart: with(plots):

>animate(polarplot,[sin(3*t),t=0..x],x=0..Pi,thickness=3,frames=20);

Right click on the plot, Animation-> Play

or click on the plot, and press the "Play the animation" button on the toolbar.