text: ## Hints for Run Time...
  
  Hi
  
  How we can reduce run time for Cases III and IV ? (Maple 2016)
  
  Thanks alot
  
  Formula_II.mw
  
  ## Curve Length 2d 3d...
  
  Good morning, I am trying to graph the length of the curve but Maple gives me an error. Please if someone can tell me how I can graph the curve in 2d and 3d.
  
  plot([t*sin(t), t*cos(t), (2*sqrt(2))/3*t^(3/2),t, t = 0 .. Pi]) -> error
  
  ## As a small exercise line y wanted...
  
  Just one more small geometry task to get to know Maple a little better:
  In the 1st quadrant, point A is on the y-axis and points B, D, C are at a positively increasing distance from the origin on the x-axis. Let BD = DC = s/2 and angle ADB = 45°. Point D is therefore the center of BC. The area of ​​triangle ABC is 60, line AD = x and the length of AC = 19. We are looking for the length of line AB = y.
  
  ## Roots wanted ;-)...
  
  A student wakes up at the end of the lecture and just catches the professor saying:
  "... and the roots form an arithmetic sequence."
  
  On the board there is a 5th degree polynomial as homework, but unfortunately the student only manages to write down
  x^5 - 5x^4 - 35x^3 +
  before the professor wipes the board.
  
  But the student still finds all the roots of the polynomial.
  
  And the roots now have to be calculated.
  
  ## How can I make the list into environment \begin{en...
  
  I have a list
  
  mylist := [[sqrt(-5*x^2 - 5*x - 1) = -4*x - 1, {-1/3, -2/7}], [sqrt(-5*x^2 - 5*x - 1) = x + 1, {-1/2, -2/3}], [sqrt(-5*x^2 - 5*x - 1) = 4*x + 3, {-2/3, -5/7}], [sqrt(-5*x^2 - 5*x + 4) = -5*x + 3, {1/2, 1/3}], [sqrt(-5*x^2 - 4*x + 2) = -5*x + 2, {1/3, 1/5}], [sqrt(-5*x^2 - 4*x + 2) = -2*x + 1, {-1/3, 1/3}]]
  
  I tried
  latex(mylist) and get
  
  \left[\left[\sqrt{-5 x^{2}-5 x -1} = -4 x -1, \left\{-{\frac{2}{7}}, -
  {\frac{1}{3}}\right\}\right], \left[\sqrt{-5 x^{2}-5 x -1} = x +1,
  \left\{-{\frac{2}{3}}, -{\frac{1}{2}}\right\}\right], \left[
  \sqrt{-5 x^{2}-5 x -1} = 4 x +3, \left\{-{\frac{5}{7}}, -{\frac{2}{3}}
  \right\}\right], \left[\sqrt{-5 x^{2}-5 x +4} = -5 x +3, \left\{{\frac
  {1}{2}}, {\frac{1}{3}}\right\}\right], \left[\sqrt{-5 x^{2}-4 x +2} =
  -5 x +2, \left\{{\frac{1}{3}}, {\frac{1}{5}}\right\}\right], \left[
  \sqrt{-5 x^{2}-4 x +2} = -2 x +1, \left\{-{\frac{1}{3}}, {\frac{1}{3}}
  \right\}\right]\right]
  
  
  
  How can I get  a latex like this?
  
  \documentclass[12pt,a4paper]{article}
  \usepackage[left=1.5cm, right=1.5cm, top=2cm, bottom=2cm]{geometry}
  \usepackage{fouriernc}
  \usepackage{enumitem}
  \usepackage{amsmath}
  \begin{document}
  Solve the following equations:
  \begin{enumerate}[label=\arabic*)]
  \item $\sqrt{-5 x^{2}-5 x -1} = -4 x -1.$ \hfill Answer: $\left\{-{\dfrac{2}{7}}, -{\dfrac{1}{3}}\right\}.$
  \item $\sqrt{-5 x^{2}-5 x -1} = x +1.$ \hfill Answer: $\left\{-{\dfrac{2}{3}}, -{\dfrac{1}{2}}\right\}.$
  \item $\sqrt{-5 x^{2}-5 x -1} = 4 x +3.$ \hfill Answer: $\left\{-{\dfrac{5}{7}}, -{\dfrac{2}{3}}\right\}.$
  \item $\sqrt{-5 x^{2}-5 x +4} = -5 x +3.$ \hfill Answer: $\left\{{\dfrac{1}{2}}, {\dfrac{1}{3}}\right\}.$
  \item $\sqrt{-5 x^{2}-4 x +2} = -5 x +2.$ \hfill Answer: $\left\{{\dfrac{1}{3}}, {\dfrac{1}{5}}\right\}.$
  \end{document}
  
  ## Loop not executing all value just taking 1st value...
  
  Loop is not executing all values just considerinng 1st value of tau0 =0.3.
  
  Also how to plot a 2D graph from the loop result
  
  Attaching sheet with questions in the sheet:
  for_loop_question_rec.mw
  
  ## transformation of PDE to ODE with special equation...
  
  i already did  a lot of function transform but this one give me some error can anyone determine what is mistake of this equation?
  
  pde_to_ode.mw
  
  ## Fixing a corrupt maple file (Maple 2022)...
  
  I have some lecture notes and examples that suddenly appears to be corrupted. I am getting the following error code when trying to open the file: "There was a problem in the loading process, you worksheet may be incomplete."
  
  I've tried the following trouvleshooting:
  
  - Close and reopen Maple
  
  - Restarting computer
  
  - Tried different computer
  
  note: I have no backup files as I do not have autosave switched on.
  
  I have also tried looking into the solution posted on a previous question on this site (https://www.mapleprimes.com/questions/235363-How-To-Fix-Corrupted-Maple-File), i.e.  changing the file format to.xml and making changes but with no luck :(
  
  Is anyone able to help me fix it and un-corrupt this file:
  
  Lecture_2_-_notes.mw
  
  ## What makes expressions containing .1e11 and 0.1*10...
  
  I cannot find an explanation why a boolean evaluation with higher Digits is not the same
  
   > restart;interface(version);
   (1)
   > Digits:=10; is(ln(.1e11*abs(-.304805898398896+1.*RealRange(.304805898398895,.304805898398897)))/ln(10) < -6); Digits:=30; is(ln(.1e11*abs(-.304805898398896+1.*RealRange(.304805898398895,.304805898398897)))/ln(10) < -6)
   (2)
   > Digits:=10; ln(0.1*10^11*abs(-0.304805898398896 + 1.*RealRange(0.304805898398895, 0.304805898398897)))/ln(10) < -6; is(%); is(ln(0.1*10^11*abs(-0.304805898398896 + 1.*RealRange(0.304805898398895, 0.304805898398897)))/ln(10) < -6);
   (3)
   > Digits := 30; ln(0.1*10^11*abs(-0.304805898398896 + 1.*RealRange(0.304805898398895, 0.304805898398897)))/ln(10) < -6; is(%); is(ln(0.1*10^11*abs(-0.304805898398896 + 1.*RealRange(0.304805898398895, 0.304805898398897)))/ln(10) < -6);
   (4)
   > 1e+10
   (5)
   > 0.1*10^11
   (6)
  
  RealRange seems to be evaluated differently.
  Any explanation for that?
  
  (expression extracted from an error message)
  
  ## Plot display in array caption...
  
  Dear Maple user
  
  I want to add caption for all four graphs with a,b,c,d at the bottom centre of each graph that should be arrange in 2X2 array and the array bottom caption as Figure 6, also i want to save the output of the array graphs in desktop with jpeg format. sample graph i have uploaded.
  
  restart:
  with(plots):
  A1:= plot(sin(x), x = -Pi .. Pi,title = "Graph at M^2=1",caption = "Fig a"):# This caption is at the centre bottom of first graph and the title of A1 is M*M (M^2)should be display
  A2:= plot(cos(x), x = -Pi .. Pi,caption = "Fig b"):# This caption is at the centre bottom of second graph
  A3 := plot3d(1.5^x*sin(y), x = -3 .. 3, y = -3 .. 3,caption = "Fig c"):# This caption is at the centre bottom of Third graph
  A4 := plot3d(1.3^x*sin(y), x = -1 .. 2*Pi, y = 0 .. Pi,caption = "Fig d"):# This caption is at the centre bottom of forth graph
  display(Array(1 .. 2, 1 .. 2, [[A1, A2], [A3, A4]]), aligncolumns = [1],caption = "Fig 6"):# This caption at the bottom centre of array graphs
  
  ## Text plotting and select from list ...
  
  I have and input parameter to a procedure called shift:=05. It sets the position of test between to points.
  
  this particular procedure has two potential sets of text one in Q and the other in vec.
  Can Q and vec have the own individual values for shift?
  
  I have shown the input to the procedure and what it outputs. The procedure itself to too long and akward to the post.
  
  Also given is the input definiton of the procedure and how I could possibly find a shift in a list.
  
   > restart
   > #with( RationalTrigonometry)
   > P1:=[-1,3]:P2:=[4,5]:
   > # shift operates as such mp:=P1+shift*(P2-P1). It's default value 0.5 It moves #   the text along between P1 and P2 # shift and shift are optional inputs to move individual test pieces. #If Q contains shift then use it else use shift   qp:=P1+shift*(P2-P1) or qp:=P1+shift*(P2-P1) #Similarily for vec
   > Qdim([P1,typeset("P1=",P1),align=[left],colour=red] ,      [P2,typeset("P2=",P2),align=[right],colour=purple] ,       Q=[Q_12,align =[below,right],shift=0.6] ,       point=[symbolsize=12,symbol=solidcircle,colour=blue,shift=0.4] ,       vec=[typeset("v[12]=",P2-P1),align=[below,right],shift=0.1],       shift=0.7):
   >
   > #The definition input of the procedure is
   >
   > #proc(P1, P2, #    {Q:=[ NULL,:-align={':-left'}]}, #        {corp::{"cart","proj"}:="cart"}, #        {shift:=0.5}, #        {vec::list:=[]}, #        {scale::{list,integer}:=1}, #        {leader::{-1,0,1}:= 1}, #        {dimoffset::{1/6,1/5,1/4,3/4,2/3,1/2,1/3,1,3/2,2,3,4,5,6}:=1}, #        {point::list:=['color' = ':-blue', symbol = ':-solidcircle', 'symbolsize' = 8]}, #        {line::list:=['thickness'=3]}, #        {plopts::list:=[]})
   > restart
   > Q:=[Q_12,shift=0.6,align =[below,right]]
   >
   (1)
   > nops(Q)
   (2)
   > for i to nops(Q) do  if has([op(Q[i])],shift) then  qp:=rhs(Q[i]);  print(i,qp);  break; end if; end do;
   (3)
   >
  
  ## Why do I have to evaluate the outer RootOf twice...
  
  The first time they are evaluated, some aborts can occur; the second time they are evaluated, no exception is thrown:
  
   >
   (1)
   > restart;
   > RootOf(         9*x1-5+RootOf(8*_Z**2+_Z-43, 41629632769253767815/18446744073709551616 .. 20814816384626883921/9223372036854775808), x1, 171590466306199/562949953421312 .. 343180932612401/1125899906842624 );
   > RootOf(         9*x1-5+RootOf(8*_Z**2+_Z-43, 41629632769253767815/18446744073709551616 .. 20814816384626883921/9223372036854775808), x1, 171590466306199/562949953421312 .. 343180932612401/1125899906842624 );
   (2)
   > RootOf(         2*x1-3+RootOf(_Z**2+2*_Z-11, 181818607464242035159/73786976294838206464 .. 363637214928484070345/147573952589676412928), x1, 301683970796757/1125899906842624 .. 150841985398379/562949953421312 );
   > RootOf(         2*x1-3+RootOf(_Z**2+2*_Z-11, 181818607464242035159/73786976294838206464 .. 363637214928484070345/147573952589676412928), x1, 301683970796757/1125899906842624 .. 150841985398379/562949953421312 );
   (3)
  
  Why does (the outer) RootOf have to be evaluated twice?