PrimeCounting(6469693230)

It never finishes computing, but smaller values work.

Is there any way to speed it up for larger values(I'm looking to do quite large values.

https://primes.utm.edu/nthprime/index.php#piofx

returns instantly.

I'm plotting some simple plots such as

plot(frac(x^2/3)*3,x=-5..5, discont=true);

Some discontinuities are connected. Using numpoints, resolution, and Digits doesn't help. Sometimes it will produce a plot with no connections but then other times it does. I need a general solution that is simple. Is there any way to refine the quality of discont?

discont=[usefdiscont=[bins=35]],

I have tried that and it seems to work but I haven't put it through the ringer. Is that all I have?

I have a list and I would like to generate all the permutations of that list deterministically and sequential. All I have found is shuffle which may duplicate results(of course I could track this to avoid dups but it should be overkill and slow and consume lots of memory).

Cl := x->max(-1,min(1, x)):

M := 25:
#-sqrt(1-x^2)..sqrt(1-x^2)
f := (x,y)->Re(sqrt(x+_i*y)):
P1 := plot3d([seq([x, y, k*f(x,y)], k=[-1,1])
], x=-1..1, y=-1..1, labels=[x,y,Rew],style=surface, grid=[200,200], thickness=2, colorscheme=["xyzcoloring", [(x,y,z)->y^2,(x,y,z)->x*y,(x,y,z)->x^2]]):
P2 := seq(spacecurve([seq([Cl(t*cos(2*Pi/M*j)), Cl(t*sin(2*Pi/M*j)), sign(k)*(abs(k) - 1.5)/140 + sign(k)*f(Cl(t*cos(2*Pi/M*j)),Cl(t*sin(2*Pi/M*j))),color=[RGB(1,t^2*sin(2*Pi/M*j)^2,1)]], k=[-2,-1,1,2])], t=0..13, thickness=4, transparency=0.7, numpoints=1500),j=1..M):

display(P1, P2);
display(P2);

The above draws a Riemann surface for sqrt(z).

The problem is that maple doesn't seem to make grid lines nicely project from the function. I added the lines myself but I cannot color them in a way that uses t. the parameter t is completely ignored in the graphing of the lines.

Also, the first graph cannot have transparency set and give meaningful results.

adding transparency=0.001 it looks like it is 10% transparent.... and going below that it just turns off all transparency. I want to barely see through the surface.

It's really hard to get a nice graph for maple. The lighting, lines, and coloring are always off to reduce the visual impact.

L := proc(N) N; end:
plot([seq(L(min(5, max(-5, 5^(x*10) + 5^(x*k))),k=0..10))], x = 0..3);

Warning, expecting only range variable x in expression max(-5,5^(10*x)+5^(x*k)) to be plotted but found name k

Removing L and everythign works. I want maple to first compute the inner expression before calling L. But even thenn it shouldn't matter in this case, it is just an identity function.

There should be no reason why this can't be done. I experience this *type* of problem with maple a lot. Where it seems to try to compute everything symbolically and breaks in some cases for unknown reasons.