@shzan  I am busy now. My answer to your question later today.

@shzan   First apply  LinearAlgebra[GaussianElimination]  command.

@H-R  Replace  2*Pi  to  6.28  in the code .  I do not know the cause of the error

@vv  for this workaround. But the error  (with  `if`)  remains. I would like to in the future releases the situation has been corrected.

@vv   I tried to apply  nth-term test for divergence   for your function f :

f:=unapply(`if`(n<10^10, 0, 10^10), n):

limit(f(n), n=infinity);

    Error, (in limit/dosubs) invalid input: if expects 3 arguments, but received 1

@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.