@viraj   

-.25965814962389295505e-49, -.39367217335124e-55, -.4842468019e-59, .1022039e-62, -.1e-68, 0., 0., -.1e-68, .1022039e-62, -.4842468019e-59, -.39367217335124e-55, -.25965814962389295505e-49

These numbers are not roots but values of the polynomial  P  in the points coinciding with found roots. As it should be, these numbers are close to zero.    

@Prof. j. smith  Remove  minimize  option, it causes an error .

An example:

Optimization:-NLPSolve(sin,-Pi..Pi, minimize);

Optimization:-NLPSolve(sin,-Pi..Pi);

@Markiyan Hirnyk  I do not think that your animation with  Explore  command can be easily made by  plots:-display(..., insequence)  or  plots:=animate   command. The problem is that all the frames have a coordinate system with the same ranges  (view  option does not work). See 

plots[display](seq(plot([x^2, 2*x-1], x = 1-a .. 1+a, view = [1-a .. 1+a, (1-a)^2 .. (1+a)^2]), a = 1.0 .. 0.01, -0.01), insequence);

@one man  I quite understand you.  Alsu, vote up from me.

PS: Markiyan, it's interesting, but unfortunately Alsu has only  Maple 12.

@Preben Alsholm   

Unfortunately for the slightly larger number  x = 10 ^ 8 , this approach does not work:

f:=x->(1+1/x)^x;

f(10^8);

evalf(%);

             Error, (in f) numeric exception: overflow

@John_Dirichlet  Briefly, in the case  unapply(f(x), x)  then  f(x) is calculated at the time of assignment, but for  x->f(x)  at the time of calling for specific  x .

Compare:

f:=unapply(diff(x^2,x), x);

g:=x->diff(x^2, x);

                                              f := x -> 2 x

                                         g := x -> diff(x^2 , x)

If you write  g(2)  then Maple just substitute  x=2  into uncalculated  diff(x^2, x) .  And we get  diff(4, 2) . That is syntax error because instead  2 (the second parameter)  should be a name.

Give specific examples with inverse trigonometric functions, in which you have issues. Then we will try to help you to use Maple to solve them.

@vv  Thanks for the link. Still seems a little odd that when using  evalf  command for an inert sum, by default generalized formal summation used instead of an usual summation (as the limit of the partial sums).

@Kitonum   with a large number of lines. The arrow was made in Paint:

R := evalc(1/(1-x-I*y)):

R1 := op(1, R), coeff(R, I):

f := unapply([R1], x, y):

F := plottools[transform](f):

A := plot([seq([convert(<cos(1/8*Pi*i), -sin(1/8*Pi*i); sin(1/8*Pi*i), cos(1/8*Pi*i)> . <t, 0>, list)[], t = -.95 .. .95], i = 0 .. 15), seq([r*cos(t), r*sin(t), t = 0 .. 2*Pi], r = 0.1 .. 0.95, 0.085)], color = red, thickness = 0, view = [-1 .. 1, -1 .. 1], numpoints = 1000, view = [-3.5 .. 3.5, -3.5 .. 3.5]):

B := plots[display](F(A), view = [0 .. 7.5, -3.5 .. 3.5]):

plots[display](<A | B>, scaling = constrained, axes = box);

@Carl Love  Thank you for your helpful comment. I had never thought about the possibility of adjusting the thickness of the gridlines. Especially I like monochrome color with thin gridlines:

y := 0: z := 0:

plot3d(abs((2*(-exp(-t-x-z)+exp(t+x+z)))/(exp(-t-x-z)+tanh((1+I)*t+(1/2-1/2*I)*y+z)+exp(t+x+z))), x = -5 .. 5, t = -5 .. 5, color = khaki, thickness = 0, axes = normal, orientation = [15, 50], numpoints = 20000);

@mskalsi  I do not know how to explain this effect.

@Vic  Maple does it automatically:

Example:

solve({x+y=0, x+y=1});

Nothing was printed.

@Abdoulaye  In this case, do a procedure with formal parameter n .

@baharm31  You wrote "It is easy to do what you did when the horizontal and vertical axis are the same size."  It is not necessary.

Example:

plot(sin(x), x=-Pi/2..Pi/2, size=[157,100], tickmarks=[spacing(Pi/4),default]);  # Font by default, size=12

plot(sin(x), x=-Pi/2..Pi/2, size=[157,100], tickmarks=[spacing(Pi/4),default], font=[TIMES,ROMAN,8]);

@acer  Thank you, very useful comment.

If we want also simplify the trig term then:

A:=y(x)=1/3/2^x+_C1/(3^x)^2 + cos(x)*sin(x):

combine(A, {power, trig}); 

                           y(x) = 1/3*2^(-x)+_C1*3^(-2*x)+1/2*sin(2*x)