restart:
f:=x->x^2-5;
v:=diff(f(x),x);
x:=1:
n:=0.0001:
err:=n+1:
 
      while err>n do
         a:=x-(f(x)/eval(v(x))):
           print(evalf(a)):
         err:=evalf(abs(a-x)):
 x:=evalf(a):
 
     end do:

An example of solving an ordinary differential equation,
expanding on what Joe Riel posted above.

A typical problem from a textbook:

Solve the differential equation y''+ y = 0 with
initial conditions of y(0)=1 and y'(0)=1 using
laplace transforms.

>restart:with(inttrans):

>d1:=diff(y(t),t,t)+y(t)=0;

d1 := diff(y(t),`$`(t,2))+y(t) = 0

 >lt_d1:=laplace(d1,t,s);

lt_d1 := s^2*laplace(y(t),t,s)-D(y)(0)-s*y(0)+laplace(y(t),t,s) = 0

 >solve(lt_d1,laplace(y(t),t,s));

(D(y)(0)+s*y(0))/(s^2+1)

 >subs({y(0)=1,D(y)(0)=1},%);

(1+s)/(s^2+1)

 >invlaplace(%,s,t);

cos(t)+sin(t)

Same answer, different format.  d/dx cot(x) is actually -csc^2(x).  Given that:

>-csc(x)^2-(-1-cot(x)^2);

-csc(x)^2+1+cot(x)^2

>simplify(%);

0

Same answer, different format.  d/dx cot(x) is actually -csc^2(x).  Given that:

>-csc(x)^2-(-1-cot(x)^2);

-csc(x)^2+1+cot(x)^2

>simplify(%);

0

Thank you for the explanation.

Thank you for the explanation.

Look at the help file for "implicitplot".

>?implicitplot

>restart:

>with(plots):

>a:=10:

>implicitplot(x^4=a^2*(x^2-y^2), x=-10..10, y=-10..10,numpoints=1000);

I added the legend option to the plot command in my original reply.  My first posting omitted that.  

I added the legend option to the plot command in my original reply.  My first posting omitted that.  

You can try the convert function.  If you assigned your answer to "ans", then you can try something like this.  It might or might not give you a result that is accepatable to you.  For more information, look at the help files for the convert command.

>?convert

>ans:=exp((1/2)*sqrt(-2*Lp*Cp*Lm^2*Cs^2-2*Lp*Cp^2*Lm^2*Cs-2*Lp^2*Cp^2*Lm*Cs-2*Lp*Cp*Lm*Cs*sqrt(Lm^2*Cs^2+2*Lm^2*Cs*Cp-2*Lp*Cp*Lm*Cs+Cp^2*Lm^2+2*Cp^2*Lm*Lp+Lp^2*Cp^2))*t/(Lp*Cp*Lm*Cs));

>convert(ans,trig);

Although the help menu is not available online, you can visit the documentation center and download the manuals as pdf files that you can search locally.

 Take a look at the alias command. 

alias(DD=D);

D(sin);

cos

DD(sin);

cos

Later edit.  As Robert mentions above, I would not alter the function of D.  Overall, not a good idea.

 Take a look at the alias command. 

alias(DD=D);

D(sin);

cos

DD(sin);

cos

Later edit.  As Robert mentions above, I would not alter the function of D.  Overall, not a good idea.

The Maple Applications Center has a few worksheets.  You have to log in to view them.  Search on "ternary".

This is not an "Internet" issue.  You do not have to have an internet connection to use Maple.  You will when you first install and activate it, but after that is does not matter.  As for your concern, there is an explanation here.  It applies to Maple 12 as well.