## Triple integral doesn't work...

I try to solve triple integraton in Maple with this code.

r := a + (b - a)*z/h;
x1 := sqrt(r^2 - y^2);
V := int(int(int(1, x = -x1 .. x1), y = -r .. r), z = 0 .. h);

but it leaves the last integral dz in the answer and warns: unable to determine if a*h/(-b+a) is between 0 and h; try to use assumptions or use the AllSolutions option
What is the problem?
and i need to get V = Pi*h(a^2 + ab +b^2)/3

Regards

## File open not working on Windows system...

This is new:

Maple 2024 frozen on opening recent files

Maple 2023 frozen on opening

Maple 2022 frozen on opening start page

Maple 2020 opening start page

The above system state is constant for about 30 min. Maple sessions without start page are working. I can enter code but file opeing and saving does not work. The fact that Maple 2020 is also not working makes it unlikely that the Java environement is part of the problem.

I have several times restarted the system. The rest of the system is working.

Something happened to the system and I have no clue what is was and what I can do about it.

Any ideas or suggestions what I could try? Windows 10.

## ODEs:-ODESteps gives error on first order linear o...

Why Maple gives this error on solving first order linear ode using ODESteps?

 > interface(version);

 > Physics:-Version();

 > ode:=diff(y(x),x)+x*y(x)=1; ic:=y(0)=0; dsolve([ode,ic]);

 > Student:-ODEs:-ODESteps([ode,ic])

Error, (in Student:-ODEs:-OdeSolveOrder1) invalid input: too many and/or wrong type of arguments passed to solve; first unused argument is _C1

ps. also reported to Maplesoft customer support.

## ReScaliing a projective vector...

I want to rescale a projective vector. Have been using gcd on the numerators and denominators. This works in simple situations. It doesn;t work well here, admitadely the points have been just made up for the question.  Square roots seem to make it mal-preform. I run into a lot of squate roots in symbolic situations. What would be a better way? I have been wondering if frontend would help?

 > restart
 > Prntmsg::boolean:=true; Normalise_Projective_Point:=1; ReScl::boolean:=true;
 (1)
 >
 > ProjLP:=overload([       proc(A::Vector[row],B::Vector[row],prnt::boolean:=Prntmsg)       description "2 projective points to create a projective line vector";       option overload;       local Vp ,gcdn,gcdd,vp ;       uses LinearAlgebra;               Vp:=CrossProduct(A,B)^%T;#print("2nd ",Vp);       if ReScl then          gcdn := gcd(gcd(numer(Vp[1]),numer(Vp[2])), numer(Vp[3]));          gcdd := gcd(gcd(denom(Vp[1]),denom(Vp[2])), denom(Vp[3]));          Vp:=simplify(Vp*gcdd/gcdn);       end if;       if Prntmsg then          print("Line vector from two projective points. " );       end if;       return Vp       end proc,       proc(A::Vector[column],B::Vector[column],prnt::boolean:=Prntmsg)       description "2 lines to get intersection projective point";       option overload;       uses LinearAlgebra;       local  Vp;            Vp:=CrossProduct(A,B)^%T;                   if Vp[3]<>0 and Normalise_Projective_Point<>0 then            Vp:=Vp/Vp[3];       end if;       if Prntmsg then            print("Meet of two Lines ");       end if;       return Vp    end proc       ]);
 >
 (2)
 > #maplemint(ProjLP)
 > pt1:=: pt2:=: pt3:=: pt4:=:
 >
 > l1:=ProjLP(pt1,pt2)
 (3)
 > l2:=ProjLP(pt3,pt4)
 (4)
 > l3:=ProjLP(pt1,pt4)
 (5)
 > l4:=ProjLP(pt2,pt4)
 (6)
 > pl1l2:=simplify(ProjLP(l1,l2))
 (7)
 > pl2l3:=simplify(ProjLP(l2,l3))