Glad you found our FAQ site!  Since you disabled the ANLL for Maple, you shouldn't have to terminate the jogamp processes through the Task Manager the next time you open Maple (the disabling has to be done prior to launch in order for it to take effect).  If this isn't the case, please contact us at support@maplesoft.com.

Please see the FAQ page that addresses this: Scaling issues when using high resolution monitors on a Windows machine

In general, using a leading uppercase character on certain commands is the Maple way of accessing the inert form of such mathematical expressions, which prevents Maple from evaluating it until you tell it to.

In this case, you are actually applying the inert form to both an integral and a sum (notice the greyed out sigma and integral symbols - if you copied this expression from another file, you get this effect by right-clicking on an expression and selecting "2-D Math" > "Convert To" > "Inert Form"). 

Forcing Maple to evaluate nested inert forms in a separate call changes the order of evaluation that Maple chooses when the expression in enter in evaluated/active form (as indicated by the use of the LerchPhi function), which can obviously lead to different results.

Hi Clara,

Our new FAQ site has a page that covers the most common sources of start-up issues.  Some of the issues only apply to Windows computers, but many of the suggestions can be applied to Macintosh computers.

If the suggestions on that page do not help, please contact support@maplesoft.com.  Be sure to include answers to the relevant questions on that page, and screen shots of any error messages.

The following will work for most optimization problems, but in this particular problem, there is an HFloat issue:

obj := (k[m]*a-(a*r*k[m]-a*k[m]-b*c-b*c[m])/(2*(-1+r)))*((1-r)*(a*r*k[m]-a*k[m]-b*c-b*c[m])/(2*b*(-1+r))-c-c[m]);
cons := {a >= 0, a >= b*c, b >= 0, c >= 0, r >= 0, k[m] >= 1, k[m]*a >= (a*k[m]*(-1+r)-b*(c+c[m]))/(2*(-1+r)), r <= 1, a/b <= (c[m]+c[r])/(k[m]*(-1+r)-r+1), a/b <= (c+c[m])/(k[m]*(-1+r)), (c+cm)*b+a*k[m]*(-1+r) <= 0};
Optimization:-Maximize(obj, cons);

If you are sure that the set-up is correct, you can try direct search.

I can reproduce this in 2017 as well, but I also noticed that the graph generated by Explore() stays within the collapsed section if you have the section open when you execute, then close it afterward.  If you have multiple sections, you may want to use the "Collapse All Sections" option in "View" > "Sections".

The situation you described is likely a bug though, so I'll submit a bug report.

The only way to (partially) recover a corrupted file is to open it in a text editor and remove the corrupted aspects.  As Christopher2222 mentions, there is no content of any kind when you open the file (even in a text editor), so unfortunately, there is nothing that can be recovered.

1. You can report potential bugs to support@maplesoft.com.
2. I can't reproduce the issue in your images; Ctrl+Space and Enter both complete "whattype" from "what" as expected.

There were a few things I noticed:

1. sys was defined twice, so the first line is unnecessary, but diff(1, t) = 0 is simply a true statement, so I'm not sure what you're trying to do in the first line.
2. In the second definition, the second "equation" is just an expression.
3. No differentials are given for b(t).
4. DEplotis part of the DEtoolspackage, so the package needs to be referenced/opened at some point in order for DEplot to work.

A sample that runs:

sys := [diff(a(t), t) = 1.342398800*10^5*a(t)+89591*b(t)+44647, diff(b(t), t) = 44647*a(t)+44902*b(t)+44859]; 
DEtools:-DEplot(sys, [a(t), b(t)], t = 0 .. 16, a = -16 .. 16, b = -16 .. 16, color = magnitude, title = `Stable Limit Cycles`, arrows = curve, dirfield = 800, axes = none)

As Dr. Manfred mentioned, this is likely the result of the bug in KB4034664.  Today, Windows released another update to resolve the issue.

Using .mla is a good idea, but you may want to consider using the savelib command.  For example:

restart;

lib := "C:/Maple Files/mylib.mla";

M := module()
  option package:
  export f, g:
  f := x -> cos(x):
  g := x -> sin(x):
end module:

savelib( 'M', lib );

restart;

lib := "C:/Maple Files/mylib.mla";
libname := libname, lib;

f(x), g(x); # f(x), g(x)

with( M );

f(x), g(x); # cos(x), sin(x)

In the debugger window, you will see a checkbox for "Copy Results on Exit".  Be sure you have it unchecked, and avoid clicking on "copy".

If you look at the LSSolve help page, you will see that the optimalitytolerance option is not available when the problem is linear.

Since your ICs don't use any actual constants, leave them out in the call to dsolve(): dsolve(diff(p(h), h) = A/(B+C*p(h)));

As far as I can tell, simplify() is doing exactly what you'd expect: simplify the expression (in this case, by factoring).  Were you expecting a different result?