I have a very simple procedure that I wrote to get information for an inequality using data from two lists, upon which I can create a pointplot . Now I know people will see what I have done and probably cringe, and believe me I do as well. I know it is not efficient and there is probably a numerous number of ways to do it better but my procedural skills for Maple are lacking. 

From my file you will see what I am attempting to do,nonetheless I will mention it here. I have two lists X,W. for each value in X I want to fine the value in W that yields F(X,L)<G(X,L) where F(X,L) is a complicated integral that I have to evalute numerically, I have tried using unapply as outline in https://www.mapleprimes.com/questions/229070-How-Can-I-Speed-Up-This-Numerical-Integral it however only made my problem worse. For small lists it seems to be reasonable but for larger precision it is not the useful. I have looked through the ?do help page and some other resources but to no avail. From what I have seen though I believe I should be using the until command in do but I can't figure it out with having two lists. 

Any help,tips or tricks will be greatly appreciated.

NumericScale.mw

I have a function that I want to plot from x=0..5 , when I ask it to plot over this range it will not plot from x=0..1 it will just go from x=1..5. However, If I ask it to plot from x=0..1 it will plot that... so then I have to splice the images together in display. 

Has anyone seen this problem? Is it something easy and stupid that I am missing? 

Function of interest attached in file. 

PlotIssue.mw

I was unsure if this should be a post or a question, or how to word it properly as I feel the attached file is the best way to see my issue. 

 However, when doing a computation involing the D_ specifically D_[mu](F[~mu,~nu]) where F is a tensor, Maple is putting in strange "variables" into the output of my expression. I set the spacetime variables myself to tau,x,y,z and in the output there is combinations which appear as x(tau),y(tau) which has completely baffled me. 

Any ideas/help would be greatly appreciated. 

EinsteinPert.mw

EDIT: The problem is resolved when the Physics[Vectors] package is removed and replaced by VectorCalculus for the Lapacian. Still curious as why the Physics[Vectors] package causes this issue. (I of course could just brute force the Laplacian but I thought I would use the power of Maple for this).

I would like to collect in derivatives of a function(s) in a worksheet where I have the Physics package loaded but It does not want to do it. When I bring the expression to a blank worksheet it does everything just fine. Am I missing something small? Or is there additional commands/options I need to input? 

Thoughts?

CollectDiff.mw

I am trying to define a Tensor expression in the physics package but it seems to be taking eons to do so, it has been running for quite some time but still no result to the point where I halt the computation. 

Does anyone have any ideas on how I could accelerate the process? 

I have attached the file I am working with. 

Define.mw