Your first line, under the command with(plots): has an error in the range.

p1:=plot(sin(x),x=-2*Pi...2*Pi,tickmarks=[0,0],color=black):

should be

p1:=plot(sin(x),x=-2*Pi..2*Pi,tickmarks=[0,0],color=black):

You have an extra dot between -2*Pi and 2*Pi.  I do not know if this will fix anything, but it does not help.

Later edit.  This does not matter.  It will not fix the LaTeX issue.

For your textplot question, here is an example that you can modify for your own use. 

restart:
with(plots):
p := plot(sin(x), x = -2*Pi .. 2*Pi, tickmarks = [0, 0], color = black):
t1 := textplot([4*Pi*(1/3)+1, 1, typeset(''y = 2*cos((1/2)*x-(1/6)*Pi)'')], align = above):
t2 := textplot([5, .5, typeset(''y = 2*cos(x/(2*Pi))'')], align = above):
display({p, t1, t2});

You can play with the location values to align the equation wherever you want it.

The above will not work with the Classic V12 interface.  Only with the Standard interface.

In Maple 12.  Plot your function:

>plot(sin(x),x);

Right click on the plot.  Go to Axes, then select Properties.  Uncheck the box that says:  Let the renderer chosse tickmarks.  Clcik the Custom Spacing Circle.  Then check off the box that says: Multiply by Pi.  If the default range is not long enough, then you can change it by assinging a range value to x.

>plot(sin(x),x=-15..15);

I believe this is available in Maple 11 as well.  If you are using an  earlier version, then see this link.

Define the nth derivative value.  Then use that in the call to diff.  Example below.  See the help pages for diff for more info (?diff).

>restart:

>n:=5;

>diff(sin(x),x$n);

This will take the 5th derivative of sin(x).

The stats package has been superseded by the Statistics package.  I also mentioned the CurveFitting package in my original post.  The code below will display the scatterplot and the line going through the data using a least squares fit, on the same plot.

>restart: with(Statistics): with(plots):
> x := [1, 2, 3, 4, 5, 6, 7, 8, 9];
> y := [4.9, 4.8, 5.1, 5.0, 5.5, 5.5, 5.7, 6.1, 6.1];
> Q := ScatterPlot(x, y):
> R := ScatterPlot(x, y, fit = [m*t+a, t], thickness = 3):
> display(R, Q);

 Example:

>restart:

>with(VectorCalculus);

>v1:=<1,2,3>;   v2:=<-3,-2,-1>;

>(v1)&x(v2);

or

>CrossProduct(v1,v2); 

Take a look at the help files for the CurveFitting package.  There are many options.  What kind of line are you looking for (straight, curved, piecewise...)?

Enter the command below and hit the Enter key, or search for it using the help browser.

?CurveFitting

What version of Maple are you using?  I used v12 for the above. 

>DEplot([r1, r2], [x(t), y(t)], t = 0 .. 1.4, [[x(0) = 1, y(0) = 1]], animatefield = true);

Take a look at the examples that come with the help file.  ?DEplot for more details.

>restart: with(DEtools):

>r1 := diff(x(t), t) = (x(t)-y(t))/sqrt(x(t)^2+y(t)^2);

>r2 := diff(y(t), t) = (x(t)+y(t))/sqrt(x(t)^2+y(t)^2);

>DEplot([r1,r2],[x(t),y(t)],t=0..1,[[x(0)=1,y(0)=1]]);

The initial conditions are in the square brackets at the end of the DEplot command.  Change them as needed.

You can visit the Maple Application Center and download an example worksheet that does exactly what you are looking for.  It can be found here.  You have to register yourself as a user in order to access and download content. 

>restart: with(plots):

>eq1:=5-abs(2*x^2+2*y^2-13);

>implicitplot(eq1, x=-3..3, y=-3..3);

Is the plot generated by the above code what you saw using the plot assistant?  Don't forget to load the plots package.

Can you give an example of the numbers that you used with the Maple igcd command and the times that were reported for the computation.  igcd is a built in command so there are no details available using the "showstat" command. 

You are trying to verify that a statement is true.  Using problem 2 as a starting point, look at your "y" term:

y:= x*cos(x)

then look at your "y prime term":

y':= cos(x) - y * tan(x) 

Start by using "diff" on your y term.  Then set that answer that you get from using "diff" as the left hand side of an equation, and substitute y:= x*cos(x) into the right hand side (cos(x) - y * tan(x) ) of your equation.  Subtract the right hand side from the left hand side.  Simplify.  You should get 0.  If not, then the original statement is false.  

I am assuming that by verifying, the question is asking you whether or not the statements are true or false.  Attach some code that you have tried for further assistance.

 >?diff

for help on using diff with some examples for higher order derivatives, like problem 1.

Try fsolve instead of solve for a numerical answer.

>fsolve(diff(2*Pi*(x+1)*(ln(sqrt(x)+1)),x$5)=0,x);

2.758918937

or after calling solve, and getting an answer in terms of RootOf, use evalf.

>solve(diff(2*Pi*(x+1)*(ln(sqrt(x)+1)),x$5)=0,x);

RootOf(32*_Z^6-175*_Z+17*_Z^4+125*_Z^5-35-250*_Z^3-330*_Z^2,1.660999379)^2

>evalf(%);

2.758918937

As Robert mentions above, your problem does not have a solution.  A similar thread here has an example that is similar to your problem.  The exact set up for your problem would look like this.  solve will not return an answer.  This is for illustrative purposes only.

>restart:

>A:=Matrix(2,2,[[2,3],[1,4]]);

>B:=Matrix(2,2,[[1,0],[0,1]]);

>X:=Matrix(2,symbol=x);

>solve(convert(X.A.X^%T-B,set));