For ease of reading I have translated the question:

A homogeneous bar AB of mass M and length 2a placed in a vertical plane can rotate without friction around its center of mass G coinciding with the origin O of a reference frame Oxy with the y-axis oriented upwards. On the y-axis, a material point P of mass m is constrained to slide, without friction. The position P is connected at the extremes A and B by means of two springs of negligible mass and length at rest and elastic constants ka=k and kb=2k, with k>0. In addition to elastic forces, the system is subject to gravitational force.
Using as generalized coordinates the y ordinate of the point P and the theta angle that the bar forms with the positive x axis [see figure], we ask:

  1. The Lagrangian of the system.
  2. The Hamiltonian of the system.
  3. Hamilton's equations.

@Samir Khan thanks for the response.

What I'm saying is, without knowing the structure of the mapleflow document, you wouldn't know how to use the variables within. 

Actually, a pdf of the mapleflow document is all that would be needed to interpret it within Maple.

Thanks Carl and Acer.  It seems part of the ordering jumble occurs because people can respond with a comment or a reply n the middle of a thread or reply as an answer to the main question.  We have 3 options with which to respond - some responses could be answering a question posed in a comment from a second answered thread group, in the first answered thread grouping.  So, reading from start to finish you might end on a question that was answered earlier on.

Anyways, the pull down order alleviates some of the issues.

Can the order of the answers and questions just be left alone so they don't go out of order?

I also noticed the arrows for sliding the windows are now gone.  Was that a design change or did I miss that update notice?

Also there must be some command line we could put into a maple.ini file to simulate clicking the
"Minimize/Maximize ribbon"   icon, isn't there? 

Aha! ok thanks.  That's a rather odd spot to put it. 

@Geoff In Maple 2020 at least unchecking the Toolbar under the view menu makes it hidden for any future sessions opening Maple.  I'm thinking it might be the same for the hiding the ribbon bar as well.

@Rouben Rostamian  I think I sort of tied in a response to below regarding if user input assumptions have to be a requirement or if there could be some coding change to allow the calculation to happen without assumptions. 

@dharr fair enough.  If the points were generated by some other calculation, yes then of course. 

However .. if .. the points at some time became collinear, the area of such an arrangement should calculate the area as zero.  Instead I receive the error

Almost like the answer should be given like a piecewise answer, 0 if collinear and some equation if not collinear.  I'm not sure that makes sense.  I guess what I'm trying to say is .. should (or could) the internal maple coding be changed so that calculations can be carried out without the users input assumptions, or must the assumptions always be stated?

So this brings up a question. 

When using a triangle command shouldn't the assumption automatically decide they aren't collinear?

@dharr oh ok thanks. 

You might get a faster response if you post your worksheet, or if you at least have an equation available for people to cut and paste.  Makes it easier for people to help.

a := [sqrt((Beta*rho*xi__8^2 - beta*xi__8^2)/xi__8) = sqrt(beta*rho - beta), (-rho + 1 + sqrt(Beta*rho*xi__8^2 - beta*xi__8^2))/(xi__3*xi__8 - 1) = sqrt(beta*rho - beta), -(-rho*xi__3*xi__8 + sqrt(Beta*rho*xi__8^2 - beta*xi__8^2) + xi__3*xi__8)/(xi__8*(xi__3*xi__8 - 1)) = rho - 1]

I've made the effort to at least make your equation easy to work from instead of the image you posted.

@acer Thank you.

Sorry I was exploring more and came across an instance I couldn't figure out.  But fontweight answers my question exactly.  Thank you very much!  I appreciate your input.

*** edit add***

To clarify my confusion, under the plot options font is where I would have thought to use fontstyle or style. 

Again though, thank you for clearing up my confusion.  Much appreciated!

Can not get the style or fontstyle as bold or any option to work.  Is there a trick? 

@acer Interestingly, the help page does not have a full list of the exported commands of package Typesetting anywhere that I can find.  Any occurances of with(Typesetting) is supressed with a colon.  It was only late last night when I had time and access.