@maple2015  Because Maple simplifies  (sqrt(x-1)+1) + (1-sqrt(x-1)) = 2  and forgets about the domain x>=1 . Of course it was a mistake Maple.

Addition: The similar example

is(x/x=1);

    true

Maple automatically simplifies  x/x  into  1  and  forgets that  x  should be not 0

@Markiyan Hirnyk   Your recent comments like trolling, so I stop this discussion.

@Markiyan Hirnyk   Because  x= 0.02612014634  does not belong to  0.01338216460 < x and x <= 0.02612014630

@Markiyan Hirnyk  For  i=14

fsolve(p[14][2] = VP[14]);

                0.02612014634

Compare with the range  0.01338216460 < x and x <= 0.02612014630

For  i=2

fsolve(p[2][2] = VP[2]);

       0.4793595141

The corresponding range  0.3166653569 < x and x <= 0.4793595141

@acer  Thank you very much for the detailed analysis of the situation with floats.

@Markiyan Hirnyk  Your example does not contradict anything. By default  Digits=10 so

is(4.=4.+10^(-20));

              true

Or use quotes:

plot( 'myproc(300,V)', V=0.1..0.9 );

Maximize(
'myproc(300,v)',
v=0.00001..0.99999
);

@acer   Thanks for  Explore ! This tool is very interesting. I did not know (as well as Rouben) about it.

@mathnoob1  For clarity, you can make all the different colors: text in black (by default), 2d-math input in red, output in blue (by default).

Example:

and so on.

See the solution here

@abbeykabir  The error in the line   y[j]:= y + h*fxy(a,b):

The name of indexed variable  y[j]  coincides with formal parameter  y
 

@smith_alpha   

f:=x^2*exp(-1.2*x);

M:=[maximize(f, x=0..100, location)];

a:=M:  L:=[2,1,1,1,2]:

for i in L do

a:=op(i, a);

od;

Of course, all these steps I'm doing in the mind.

@Markiyan Hirnyk  http://dxdy.ru/topic19074.html

@Markiyan Hirnyk  I think that your moralism out of place in our community. You are not a teacher at school and I'm not your pupil.

@Markiyan Hirnyk  See links on request  "задача о жуках в вершинах квадрата"  here