Instead of Kitonum's f, we can use

anotherF := x-> ifelse( 0=frem(x+2, 4), undefined , x- 4*floor( (x + 2)/4 ) );

although this is a tiny change.

Is this one of answers ?

subs(B=1-d, algsubs( 1-d = B , A*(-1+d)/r^(1+d)));  
            
                                    A (1 - d)                   
                                  - ---------                   
                                     (1 + d)                    
                                    r

What is your purpose in factorization?

Is the following your answer ?

> myEq:= (A/T)^(1/k)*(T/phi)^(beta/k):                 

> simplify( myEq^k, power,symbolic);                                            

                              (-1 + beta)    (-beta)                            

                           A T            phi                                   

> %^(1/k);                                                                      

                           (-1 + beta)    (-beta) (1/k)                         

                       (A T            phi       )                              

> 

What is your "subplot"? Is the following link helpful for you ? 

http://www.maplesoft.com/support/help/Maple/view.aspx?path=plot/arrayplot

amplestd2e.sty ??  

Instead of maplestd2e.sty ?

The location of maplestd2e.sty depends on your OS.

If your maple is  "Maple 2015 (X86 64 LINUX)",  the location is 

(The installed directory of Maple)/etc .

Because both expressions are indefinite integrals.

As for "GAUSS-ELIMINATION", please check the following:

http://www.maplesoft.com/support/help/Maple/view.aspx?path=LinearAlgebra%2fGaussianElimination

I cannot understand  the rule of making DD.  

As for C,  is the following OK ?

LinearAlgebra[DiagonalMatrix]([Matrix(3,symbol=C,shape=symmetric),C[4,4],C[5,5],C[6,6]],shape=symmetric);

or

LinearAlgebra[DiagonalMatrix]([Matrix(3,symbol=C,shape=symmetric),op(convert(LinearAlgebra[SubVector](ArrayTools[Diagonal](Matrix(6,symbol=C,shape=symmetric)),4..6),list))],shape=symmetric);

LinearAlgebra[Transpose] () does not help you ? (This is a just irresponsible idea.)

All you need do is to write a procedure which returns

(Matrix(2,2,[a,b,c,d]))^(-1)

> Optimization[Minimize] (1/x*ln( (1+3*x)/(1-x) ), x=0.1..0.9);

[3.21874108833696, [x = 0.507125792764503]]