For comparision:
The best I could do with substitutions. What makes it tricky is the coefficient R1*R2 of s.

I spare out the sorting detail since its already twice as long as acers solution.

Download subsway.mw

Your parameters still do not match. In the following I have tried to show how the substitution should be done and what needs to be changed.

Download parameter_mismatch.mw

In your simple example 

L1 := -L*(k - 1);
collect(L1, L);
                           (-k + 1) L

preserves a "simplified" factor (sign of your original factor has changed). Collect should also work in more complex cases unless there are other sub-expressions where you don't want to collect L. In those cases changing the sign of the factor like this

Lm := (simplify(k*sqrt(L*L)) assuming (0 < L));
L1 := (factor(-L + Lm) assuming (0 < L and 0 < Lm and 0 <= k));

might work as well.

Infolevel confirms that dsolve integrates a first order ode

intde := int(x^2*diff(y(x), x)/(x^2 - 1), x) = int(y(x)^(1/2), x)^(-2/3);
infolevel[dsolve] := 5;
dsolve(intde);
Methods for first order ODEs:
--- Trying classification methods ---
trying homogeneous types:
differential order: 1; looking for linear symmetries
trying exact
<- exact successful

If you additionally increase printlevel up to 50 you will find the ODE (which can also be derived by differention of the original equation w.r.t. to x).

Edit: In this way Maple reduces the inital equation to a first oder equation.

Then appropriate methods are applied

This is the first order integroDE Maple integrates. An ODE without integral that integrates to the same result would be this one

To get there, you have to find a way to convert the right handside of your problem like this (i.e. getting the integration out of the denominator): 

The attachment shows where the above right hand side comes from.

integrode_backward.mw

A base like that with a z-axis?

Any preferences on the ranges?

You did not give a motivation why you use min in your example on a list without units. I  assume that you want to use min on lists with and without units after loading the simple package.

Until the bug is fixed you could call the default environment for lists without units by adding the prefix :- to min:

with(Units[Simple]);
:-min(0, 0);

I run your code in Maple 2023 and have corrected a few errors. What I did is highlighted in oragne.

I had no time to check why A is larger than 1 but maybe my touchups help in further analysis.

A_less_than_one_reply.mw

Alt s with the search term "conic" provides some usefully resources.

For algebraic expressions help(geometry,conic) provides ouput like this:

You may perhaps not have noticed that the call print[-2]() sets the interface variable prettyprint.

Calling print without argument is maybe not an intended use.

I will send a software change request for the interface prettyprint call.
 

Download reset_interface.mw

I tried 2022 and 2023 with the same outcome that you described.

Maybe I found an explanation why Maple.ini does not work:

Any Maple command in Maple.ini, Startup Code and userprofiles is passed directly to the kernel (but not via the GUI).

Typesetting:−Settings(parserwarnings=false): seems to instruct the GUI not to issue a warning on the input (before the command is send to the kernel).

If this is correct, you are looking for a new feature that initializes the GUI. Kind of a GUI.ini or a button (maybe I overlooked it) in the options.

Try

Optimization:-Maximize(y)

I forgot:

From help(Temperature)

Combinations of Temperature objects that are neither affine nor null can be valid as intermediate results of a computation, but they do not typically represent physical concepts. In order to indicate this, they are displayed in red.

combine does remove the unit K in the brackets of the temperature object and adds a unit m (do not ask me why) and then turns everything into red to warn the user).

Instead of using a temperatur object I inserted 90 F from the units pallete. This works and no red output is returned.

If you want to use a previously defined temperature object you can to do it this way.

Temperature(90, Unit(degF));
params := n = Unit('mol'), T = Value(%)*Scale(%), P = 101325*Unit('Pa'), R = evalf(Constant(R, units));

For the second remaning question use convert or simplify

I had this issues on Windows 10 more than 2 y ago and than it dissaperad as it came.

At the time I attributed this to something on the system level when Windows file explorer was attemtping to connect to network drives (which were temporailiy not available).

About a month ago, I had the problem again and did what Joe Riel suggested. I also noticed that the problem occurred right after system restart and it took a while for Maple to start the first instance of mserver.exe (maybe there is some house keeping going on in the background). After that, Mapel worked fine.

At least I am not the only one.

To plot the Maple onliner

plot3d(-2 - sqrt(3)*tanh(1)*tanh(n - 6*tanh(1)*t), t = -5 .. 5, n = -5 .. 5)

something like that should work

% plot grid
t = linspace(-5, 5, 100);
n = linspace(-5, 5, 100);

% compute plot grid values
[T, N] = meshgrid(t, n);

% compute Z values
Z = -2 - sqrt(3)*tanh(1)*tanh(N - 6*tanh(1)*T);

% plot
surf(T, N, Z);

(I don't have Matlab running to test.)

For anything beyond, a Matlab forum can probably provide more answers.

should give you the answer

with(geometry);
_EnvHorizontalName := 'x';
_EnvVerticalName := 'y';
ellipse(p, ['foci' = [[-1, -1], [1, 1]], 'MinorAxis' = 2*sqrt(14)]);
Equation(p);

but does not accept the way I define the foci... Maybe someone can tell whats wrong with it