Regarding your 3rd point, Maple can be customized in many ways, check help pages for the commands interface and kernelopts. Also, in Maple type ?worksheet,reference,initialization on how to create an initialization startup file.

If you have a whole company switching over to Maple, you should consider getting in touch with Maplesoft for a customized training, i.e. webex sessions or onsite visits.  

Do you mean you can't figure out the purchase process in the Maplesoft webstore https://webstore.maplesoft.com?

You should directly contact customer service, answering such questions is their job: custservice@maplesoft.com

In case you have Maple 2019, you could check out the new options for drawing polygons

https://de.maplesoft.com/products/maple/new_features/Maple2019/Visualization.aspx

f:=sin(4*pi*w)/sin(2*pi*w);
int(diff(f, w), w);

You may as well use keyboard shorcuts, i.e. press A, then cntrl-alt-o to enter overscript (international keyboard layouts). See shortcut keys in Help menu for details, or type ?2dmathshortcutkeys

There is not really an option for a line based filling, try instead a shading like this: 

plots:-shadebetween(x^2, x + 5, x = -5 .. 5, color = "Blue", view = [-5 .. 5, -1 .. 10], negativeonly, size = [500,500], scaling = constrained, thickness = 3, changefill = [colour = "Orange"]);

Still, you would need another command like textplot to mark your intersections with letters. Or use a paint program to do graphical and text based modifications.

This works using angle brackets, use single bars to separate column vectors. But I find nm's way less prone to errors, therefore better.

aSys:=StateSpace(<<1,2>|<3,4>>,<<2,3>>,<<1,0>|<0,1>>,<<0,0>>);

You cannot move pictures around, but from menu you can choose insert->table at your preferred worksheet location and insert a multi column/row table to generate a grid, where you have some freedom to place inside you pictures and related text or commands. Then you can make table border color as background to make the grid (or portions of it) invisible.

Another way:

exp(`%-`(x) + `%-`(y));
expand(%);
value(%);# to unfreeze

Example:

A := Matrix(3, 3, [1, 1, 1, 2, 2, 2, 3, 3, 3]);
DF := DataFrame(A, columns = [D1, D2, D3], rows = [D1, D2, D3]);
Tabulate(DF, width = 15, exterior = none, fillcolor = white, color = blue):

You can apply allvalues() to get rid of RootOfs. Your solutions are complex, so your equation probably does not model your real world problem correctly.

Eq1 := -25.23733555*diff(h__Water(t), t) = 0.5982*(-190.1309944 - 13.64385474*h__Water(t) + diff(h__Water(t), t)^2)^(1/2); ics1 := h__Water(0) = 0.2; Sol1 := dsolve({Eq1, ics1}); allvalues(%); evalf(%);

If you apply expand to your equation, you get an 8th order polynomial equation in cos(t). Maple cannot solve it symbolically, and unless you have reason to believe that there is a symbolic solution, you probably don't need to try.

expand((1 + 1/4*cos(t))*cos(7*t) = 1/10);solve(%, cos(t));

Write elif instead of else if

a*b=a*c;%/a

type sqrt(5*``(x+1)+y) 

It also does not evaluate next time you execute it.

see ?emptysymbol