restart:

Q := x* 2500/(2+3*6^(1/2))^2/(3*6^(1/2)-2)^2;

simplify(%,[radical]);

I asked a similar question on comp.soft-sys.math.maple.  The square brackets "expand" the expression first, and then simplification occurs, w.r.t. radicals.  You can replace "radical" with "sqrt" and it will work as well.  This is not an explanation, but it will force a solution.  I have not seen any documentation on this.  If anybody has a link where this is documented, I would like to see it.

Correct.  That is the difference between it working and not working.  The rest is up to you.

 What happens if you change your last line to:

LineInt(VectorField(<x^2*y, x^3, x*y>), Path(<sin(t), cos(t), 1/4* (sin(t)^2 - cos(t)^2)>,t=0..2*Pi));

Do you get the answer that you are expecting?

Hello.  Your question is a homework problem, and having someone give you an answer would not be fair to you, your fellow students and to your professor.  At a bare minimum, show what you have done (looking at help pages, example by hand,...).  

At the Maple prompt, type the following and hit the enter key, or use the help facility and search for VolumeOfRevolutionTutor

?Student[Calculus1][VolumeOfRevolutionTutor]

Please do not ask us to do your homework for you.  None of us will benefit by it.

Start with the help pages and the included examples.  Each of the commands below will open up a help session with examples.  Try the examples, and then substitute with your equation, and check if the answer you get matches what you expect (done by hand).

?Student[Calculus1][ArcLength]
 

?Student[Calculus1][ArcLengthTutor]
 

all that razzamatazz about RootOf this and RootOfthat can be useful when there is more than one solution.  For more details, look at the help pages.  

Instead of posting a pdf, please post the actual worksheet or text that can be copied into a worksheet.  I am generally a lazy sort, and typing makes my fingers ache.

I have attached a file done with the classic worksheet.  Hope this helps.

Download 221_solve.mws

Impedances connected in parallel have the form:

1/Z = 1/Z1 + 1/Z2 + ... 1/Zn

Knowing this, you can assign Z1, Z2, ... and then use the solve command.

solve(1/Z=1/Z1+1/Z2+1/Z3+1/Z4,Z); 

restart:

convert(cos(x/3),tan):

convert(%,cos):

simplify(%);

2*cos(1/6*x)^2-1

but I am curious, what does "clean" mean here, relative to the original expression?

Try expand instead of simplify and see if the result is more to your liking.

expand(exp(x^2)*(C+(1+x^2)*exp(-x^2)));

Start by rewriting your equations, using Maple syntax, and be consistent.  For example, Cos is not the same as cos.  Below I will illustrate what this means, and then you can take it from there.

w:=Pi; yields

w := Pi

Cos[w]; yields

Cos[Pi]

cos([w]); yields

Error, invalid input: cos expects its 1st argument, x, to be of type algebraic, but received [Pi]

and

cos(w); yields

-1

which is the correct results.

Once you have your equations in the correct format, take a look at the help files for the solve command.

?solve

If you are still having problems after that, try uploading your worksheet.  The attached illustrates what I mentioned above.

Download 221_equation_syntax.mws
View file details

Start with the help file.  Enter the command below and hit the enter key:

?plots[fieldplot]

For your example, the code below will do it:

restart:

with(plots):

fieldplot( [sin(Pi*x),x*y-1], x=-2*Pi..2*Pi, y=-10..10,arrows=SLIM, color=x);

Notice that Pi is capitalized.

In Maple, ?implicitplot has an example that plots a circle.  The code below will do the same in Matlab.  There are other ways to do this as well. 

x=-1:0.1:1;
y=-1:0.1:1;
[x,y] = meshgrid(x,y);
f = x.^2 + y.^2 - 1;
contour(x,y,f,[0,0]);

If the value that you are using is stored in "x", then you can do something like this.

x=0

x=x+(x==0)*eps

log(x)*x

ans =

 -8.0033e-015
 

Try this link and see if it solves your problem.

Like this, or something else?

g := x -> piecewise(x<=1,x,x<=3,2*x,x<=10,3*x);

g(x);

plot(g(x),x=0..10,discont=true);