@Carl Love   Thanks for the detailed explanation.

Also I really liked your new one-line approach.

@J4James   Step by step solution for this integration can be done by the command

Student[Calculus1][ShowSolution](Int(exp(x)*sin(x), x));

As for  infolevel  command, I never used it. See help for this.

@acer  in acer's simplification  (unfortunately manually):

simplify(convert(evalf[9](ee), rational, exact));

subsop(5 = (exp((7/10)*r*t)*x^(7/10)+1)^2, %);

Where  the non-negativity of all the variables in your "proof"  was used? It is obvious that for arbitrary variables the inequality is not true.

@Carl Love 

Matrix.mw

@Carl Love   Should be  [T]=~[C]

@marekszpak 

A := IntegerPoints1({-1/2 < 2*f*(1/53)+7*g*(1/53), 3/106 < 7*f*(1/53)-2*g*(1/53), 2*f*(1/53)+7*g*(1/53) < -37/106, 7*f*(1/53)-2*g*(1/53) < 1/2}, [f, g]);

plots[display](plot(A, style = point, color = red, symbol = solidcircle, symbolsize = 15), plots[inequal]({-1/2 < 2*f*(1/53)+7*g*(1/53), 3/106 < 7*f*(1/53)-2*g*(1/53), 2*f*(1/53)+7*g*(1/53) < -37/106, 7*f*(1/53)-2*g*(1/53) < 1/2}, f = -2 .. 4, g = -5 .. -2, color = "LightGreen"), scaling = constrained);

@John Fredsted  The idea is the same as mine, but the implementation is much easier. I just did not know about  convert,decimal  command, etc.

@Kitonum   Continuation of the previous code:

Pic := plots[display](A, Pr, seq((Tr@@k)(F), k = 0 .. 7), C, T, axes = none):

Tr1 := (p, alpha)-> plottools[rotate](p, alpha, [[0, 0, 0], [0, 0, 1]]) :

plots[animate](plots[display], ['Tr1'(Pic, alpha)], alpha = 0 .. 2*Pi, frames = 50);

@lg674  Should be  Pi  instead of pi in your code. Also you have 4 constants  E, A, B, m  instead of 3 costants a, b, c, so the texts of the procedures should be changed.

@Carl Love  Very clear and easy solution, vote up . The same but slightly shorter and with the display of the desired results.

X:= [u,v,w,alpha,beta,gamma]:  G:=LinearAlgebra:-GenerateMatrix: 

M, Sys:= G(convert(Sys, list), diff~(X(t), t$2)):  'M'=M;

C, Sys:= G(-convert(Sys, list), diff~(X(t), t)):  'C'=C;

K, F:= G(-convert(Sys, list), X(t)):  'K'=K; 'F'=F;

@Markiyan Hirnyk  Please explain how it could happen that in the post on January 10 2016, all comments have been removed, including mine, this post has turned into a question with your answer in the form my animation?

You wrote in brackets something like this

restart;

x=solve(y, x);

                                    x=()

@vv  Why to check, we can not instead of

eval(  'evalf'( 'add'('add'(a, i=1..N), j=1..N)),  N=1000);

simply write

add(add(evalf(a, i=1..1000), j=1..1000);

The result is the same, but it requires 10 times less time. 

@Majmaj You can't use  labels = ["x values", "y values"] if axis[2] = [color = white], because everything that refers to  y-axis  will be white.