Try changing your last line to:

display([plot1, plot2], view = [0 .. 120, 0 .. 40])

and see if it meets your requirements.  I am using Maple 12, although that should not matter here.  I was not seeing a red and blue waveform with each of the individual plots.  Both were red for me.  In the animation I  could see both lines, without one of them being cut short.

Option 2:  Right click on your final plot, go to Axes, then Properties and change the Horizontal Range Max to 120.

Without the complete worksheet, it is hard to see what is actually going on.  But, looking at your code above, it looks like from the first plot structure that you are setting t = 0 .. t1, and in the second plot structure you are setting s = 0 .. t.  So, my question is, do they animate o.k. when they are not combined?  If so, then try changing your range variables from one plot structure to the next.  If not, maybe you can upload your worksheet.

Very nice.  I noticed that the command "whattype" applied to L returned "exprseq", but I didn't know what to do with that.  More elegant indeed.

You have two sets of sets.  ?list for more details.  The attached worksheet manually converts each set into a list and then using commands from the ListTools package, arrives at your final desired result.  There are probably other, more elegant ways to do this.   

Download 221_set_list_sort.mws

While not a "proof", by inspection it looks equivalent.

>restart:

>eq:=4*cos(theta)^3-3*cos(theta);

>combine(eq);

Take a look at the help files for the select command.

?select

>restart:

>L:=[1,2,3,2,4,6,5,0,9,0,3,4,4];

>select(x->x<=3 and x>1,L);

>nops(%);

In one line:

>nops(select(x->x<=3 and x>1,L));

The syntax for the select command used above was taken from the following document:

www.mast.queensu.ca/~math418/m418oh/maple.pdf

I is the built in root of x^2 = -1, that is why you are getting an error.  You can change this using the line below at the beginning of your worksheet.  Then I[pk]:=10
will work. 

interface(imaginaryunit=j):

?interface for more help on this topic

The above code, using cut and then paste into v12 works fine.

restart:

plot(x^4 + 6*x^3 + 3*x^2 + 6,x=-6..1);

solve(x^4 + 6*x^3 + 3*x^2 + 6,x);

evalf(%);

This will give all solutions, including the complex ones.

fsolve(x^4 + 6*x^3 + 3*x^2 + 6,x=-6..-1);

This will return just the x values that result in y=0.  The range was chosen

after looking at the output of the plot command.  Look at the help files for

each of the solve commands (fsolve and solve) for more details. 

replace e with exp and look at the help pages for the solve command. Each of the commands below will bring up the help pages.  There are examples there that you can use.

?exp

?solve

I think this is what is meant:

ln(exp(1));

                 1

As Axel points above this, "e" does not have any particular meaning in Maple.

verify(sin(x)/cos(x),tan(x),'testeq');

works as well.

restart: with(plots):

implicitplot(x^2 + y^2 <= 4, x=-2..2, y=-2..2,filled=true,numpoints=1000);

For more help on this, ?implicitplot

The following link to the Maple Applications Center might be usefull to you.

?plottools[ellipse]  will get you started.

This site has a similar example that you can open in Maple and examine yourself.

Scroll 2/3 of the way down the page and open the file titled FITODES2.MWS