@Markiyan Hirnyk 

For better perception must reduce the number of contours and the range for  y :

ContoursWithLabels(2*(2-x)^2*exp(-x^2-(y+1)^2)-(15*((1/5)*x-x^3-y^3))*exp(-x^2-y^2)-(1/3)*exp(-(x+1)^2-y^2), -2 .. 2, -2.5 .. 2.5, {seq(-6 .. 6, 1)}, [color = black, axes = box], Coloring = [colorstyle = HUE, colorscheme = ["Cyan", "Red"], style = surface]);

 @H-R

My answer see in this  post

@farhad-b 

1) You wrote "is there any different between f:= x(t)^2 + y(t)^2:  and  f:=t->x(t)^2+y(t)^2" ?   About that distinction, I wrote in detail above.

2) I have never worked in Matlab and do not export to Matlab, so I can not give any advice.

@Markiyan Hirnyk 

@H-R   Obviously this is a typo. Instead of  plot/options  should be  plots[arrow] .

Only here instead of  width  the option  thickness  works.

@H-R  Just open the help on  Student[VectorCalculus][TangentVector]  command and everything is there.

@Axel Vogt 

Student[VectorCalculus][TangentVector](<cos(t), sin(t)>, range = 0 .. 2*Pi, curveoptions = [color = blue, thickness = 3], output = plot, scaling = constrained,vectors=10,vectoroptions = [shape=arrow, thickness = 3, color=red, length= 0.01, head_length = 1/16, head_width=1/16]);

@vv  But it's easy to fix

p:=3.5*x^2+3.2*x-6.5+88.3*x*y-y^3+a*y + sin(1);

evalindets(evalf(p), float, round);

@asa12  Replace the line  add(zip(`*`, c, [t]));   by  add(i, i = zip(`*`, c, [t]));  

or   `+`(op(zip(`*`, c, [t])));

@Markiyan Hirnyk  for a workaround. But the reasons of bugs in  solve  command are still not clear.

@Markiyan Hirnyk  Maybe you have in mind the following expression

Expr:=expand((x^2-x-3)^10)-exp(-x);

Find all minuses in it and their number, you can, for example, by conversion to string

convert(Expr, string);

StringTools[SearchAll]("-", %);  # positions of all the minus signs

nops([%]);  # total number of minuses  

Here is an another kind of animation. It uses a circular symmetry of the surface and of course much easier to implement than acer's method.

restart;

A := r->plot3d([2*cos(phi), 2*sin(phi), z], z = 0 .. 5, phi = 0 .. r, style = surface):

B :=r->plot3d([8*cos(phi), 8*sin(phi), z], z = 10 .. 20, phi = 0 .. r, style = surface):

C := r->plot3d([(-4+(6/5)*z)*cos(phi), (-4+(6/5)*z)*sin(phi), z], z = 5 .. 10, phi = 0 .. r, style = surface):

plots[animate](plots[display], ['A'(r), 'B'(r), 'C'(r), axes = normal, scaling = constrained], r = 0 .. 2*Pi, frames = 60, lightmodel = light4);

@hossayni  If you want to build multiple plots in one place, then there is no need to use  plots[display] . Just use a list of these plots. Here are 51 plots of  sin(m*x) , m=1..2  with the step  0.02

plot([seq(sin(m*x), m = 1 .. 2, 0.02)], x=0..2, color=green, thickness=2, axes=normal);

@nMaple  In the loop, you should assign names to these plots, and then (outside the loop)  build everything by  plots[display] command:

for i from 1 to 5 do

P[i]:=plot3d( ... ):

end do:

plots[display](seq(P[i], i=1..5));

@nMaple 

1) See help   on  readdata  command.

2) I did not understand - what  kind  of animation do you want?