Even a crystal ball cannot solve a nonsensical problem. You cannot simultaneously solve n equations for more than n variables (n=1 in this case). That is a fundamental principle of mathematics. It is beyond being an undecidable problem (such as the Continuum Hypothesis or the propositions whose existence is guaranteed by Godel's Theorem). It makes no sense at all.

Following the directions given on the Wikipedia page "Weibull distribution", section "Parameter estimation", subsection "Ordinary least square using Weibull plot", I only made a single small change to your computation: I changed (i - 0.5)/n to (i - 0.3)/(n + 0.4). Anything else that may appear to be a change is merely a mathematically equivalent simplification. (In particular, there's no need to use both sort and Rank; using either one is sufficient.) Then I used Statistics:-LinearFit to do the regression.

Download WeibullParameters.mw

This Answer is fundamentally the same as the one by @nm ; I just want to give some background information.

The command evalb, when applied to an equation, checks whether the two sides of the equation are syntactically identical; but you want to check whether the two sides are mathematically equivalent.

Two expressions are syntactically identical if they are stored in exactly the same way in the computer's memory. (In Maple, in practice, this means that only one copy is actually stored at all.) Via a process that Maple calls automatic simplification, some expressions which are typed in differently will become syntactically identical:

evalb(sin(a+b) = sin(b+a));
             true

I think that you (and most other readers here) already understand basically what it means for two expressions to be mathematically equivalent. Let me try to be more precise (although this is still not a perfect definition): Two expressions are mathematically equivalent if they are numerically equal for all possible numeric substitutions of their variables for which they're both defined and which satisfy the "current assumptions". The "current assumptions", if unspecified, are all complex numbers. In Maple, assuming or assume can be used to specify assumptions. 

Of course, if two expressions are syntactically identical they are also mathematically equivalent. But the converse isn't true. It can be proven (see Richardson's Theorem) that it's impossible to create a perfect algorithm to determine mathematical equivalence. So, whether you use is, expand, simplify, or numerous other commands, there will always be undecidable cases. However, one may hope that in the cases where the equivalence is already established via a well-known and elementary theorem (such as the case you present), Maple will be able to verify it. The best command to try first is is:

is(sin(x + y) = sin(x)*cos(y) + cos(x)*sin(y));
              true

The reason that is is the best first choice is that it will give up and return FAIL if after some reasonable amount of time it cannot decide true or false. Other commands may run for an infeasible amount of time.

Regarding checking integrations: Suppose that f is the expression that you want to integrate (let's say with respect to x), and F is your proposed antiderivative that you want to check. Then do

is(f = diff(F,x));

You may need to include assumptions on x. Appropriate assumptions are likely obvious. For example,

is(f = diff(F,x)) assuming x > -1, x < 1;

There's usually no need to exclude isolated singularities such as specific values of x that make a denominator 0.

Keep in mind that the default assumption in Maple is "all complex numbers", not "all real numbers". The calculus of functions of complex variables is sufficiently similar to that of real variables that you usually do not need to make the distinction.

Download PlotSteepestPath.mw

printlevel is an "environment variable". That means that if its value is changed within a procedure, then it is automatically reset to its previous value when the procedure exits. Thus, you don't need to store the previous value or reset printlevel yourself.

What you're calling the "depth" can be measured by kernelopts(level).

I ignore your weird use of RETURN. Without it, the second integral gives true*x, whereas I'd expect false*x. There are reasonable limitations on the "depth" within an expression to which assuming can penetrate. Compare:

(coulditbe(y=1) assuming y>=0, y<=x) assuming additionally, x>0, x<1;
                              true

coulditbe(y=1) assuming y>=0, y<=x, x>0, x<1;
                             false

The first case seems more akin to your integral.

Your graph_list can be partitioned into a table of equivalence classes under isomorphism by

ListTools:-Classify(g-> [seq](op(4, GraphTheory:-CanonicalGraph(g))), graph_list)

Define the function with unapply:

f:= unapply(a*x, x)

A synonym for unapply is MakeFunction.

I assume that you're using 2D Input which you've converted to 1D for posting here. If so, then you need to remove any space characters you have after display, textplot, and draw. Also, the arguments to display need to be in parentheses. If I change your display command to

display(
    textplot(
       [
           [coordinates(S)[], "S"], [coordinates(P)[], "P"], [coordinates(H)[], "H"], 
           [coordinates(K)[], "K"], [coordinates(M)[], "M"]
       ], font = [times, bold, 16], align = [above, right]
    ), 
    draw([
        delta(color = blue), deltap(color = blue), D(color = red), c1(color = black),
        S(color = black, symbol = solidcircle, symbolsize = 16),
        P(color = black, symbol = solidcircle, symbolsize = 16)
    ]), 
    scaling = constrained, axes = none, view = [-15 .. 15, -15 .. 15]
);

 then I get this plot (for which you'll likely want to change some of the sizes):

The simplify command doesn't work on equations (except in the sense that it's mapped to the left and right sides independently). In common mathematical usage, as taught in secondary-school algebra, "simplification" is only performed on expressions, not equations.

The Python code shown in your forum link handles the minutiae of setting up grids/meshes for 3D plots and converting spherical and cylindrical coordinates to rectangular. This is unnecessary in Maple; the plot3d command handles that in the background.

(* Original Python code:

from matplotlib import pyplot as plt
from math import sqrt, pi, cos, sin
import numpy as np

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

t_grid = np.linspace(-1 - sqrt(7), -1 + sqrt(7), 50)
s_grid = np.linspace(-1, 1, 50)
T, S = np.meshgrid(t_grid, s_grid)
theta_fun = lambda t, s: 0.2 * pi * (t + 1 + sqrt(7)) / sqrt(7) - 0.4 * pi + 0.1
phi_fun = lambda t, s: pi * s / (4 * sqrt(2)) * sqrt(max(2 - t ** 2 / abs(t - 3), 0))
for k in range(1, 16):
  phi0 = 0.4 * pi * k
  r = 14 - 0.8 * k
  x_fun = lambda t, s: r * cos(phi0 + phi_fun(t, s)) * cos(theta_fun(t, s))
  y_fun = lambda t, s: r * sin(phi0 + phi_fun(t, s)) * cos(theta_fun(t, s))
  z_fun = lambda t, s: r * sin(theta_fun(t, s))
  X = np.array(list(map(x_fun, T.flatten(), S.flatten()))).reshape((50, 50))
  Y = np.array(list(map(y_fun, T.flatten(), S.flatten()))).reshape((50, 50))
  Z = np.array(list(map(z_fun, T.flatten(), S.flatten()))).reshape((50, 50))
  ax.plot_surface(X, Y, Z, cmap='Reds')
z = np.linspace(-25, -10, 50)
p = np.linspace(0, 2 * pi, 50)
Z, P = np.meshgrid(z, p)
X = np.cos(P)
Y = np.sin(P)
ax.plot_surface(X, Y, Z, cmap='Greens')
ax.set_box_aspect(aspect=(1, 1, 1.5))
*)

The original author plotted the petals using a nonstandard form of spherical coordinates that has the cos(theta) and sin(theta) exchanged, where theta is the altitude angle. I adjusted this to standard spherical coordinates by replacing theta with Pi/2 - theta. The original stem was done using standard cylindrical coordinates.

I don't know the exact details of the Python coloring function cmap. I made an approximation using plot option colorscheme and the ColorTools package.

For the lightmodel, I simply chose what looked best to me from the very limited choices (five) Maple offers. I chose an orientation that looked good to me. 

My algebraic formulas are mathematically equivalent to the Python; however, I simplified them, so they're not syntactically identical. If Python has some difference between math.sin and numpy.sin (likewise for cos), I don't know what it is. The original author used both (perhaps unintentionally).

Surprisingly, Maple has no plot option equivalent to aspect, so I used plottools:-scale, which will do essentially the same thing provided that the options axes= none and scaling= constrained are used and that one doesn't care about the actual numerical values stored in the plot.

#Maple translation:
cmap:= C-> colorscheme= ([ColorTools:-Lighten, ColorTools:-Darken] @@~ 2)(C):
aspect:= (S::And(list(realcons), 3 &under nops))-> (P::specfunc(PLOT3D))-> 
    plots:-display(plottools:-scale(P, S[]), 'axes'= 'none', 'scaling'= 'constrained')
:
k:= [$1..16]:
(aspect([1, 1, 3/2]) @ plots:-display)(
    plot3d(
        `[]`~(
            14 -~ 4/5*~k, 
            Pi*~(2/5*~k +~ s*sqrt(max(2 - t^2/abs(t-3), 0)/32)),
            (Pi*(7 - 2/sqrt(7)*(t+1)) - 1)/10
        ),
        t= -1-sqrt(7)..-1+sqrt(7), s= -1..1, coords= spherical, cmap("Red")
    ),
    plot3d(1, theta= 0..2*Pi, z= -25..-10, coords= cylindrical, cmap("Green")),
    style= surface, lightmodel= light4, orientation= [49, 52, 27]
);

Your system is far more than "a little" complicated. I think that there's no hope of solving this (with Maple or anything else). Maple will likely continue working on it until it runs out of memory, and then crash.

Yes, it's reasonable for it to run for days, weeks, etc., on such a system.

No, there's no way that multi-core processing can help with this.

I believe that both of those answers would be true for any mathematical software.

For what its worth, you can easily (nearly instatntaneously) eliminate 4 of the variables. The complexity of the remaining two equations might help you appreciate why this is unsolvable.

(Sols, Eqs):= eliminate({eq||(1..6)}, {u,v,w,x, y})[]:
print~(Sols): print~(Eqs=~0): 
 

I believe that this simple procedure handles all the cases presented so far, requiring no input other than the equation itself. It also accepts and gracefully handles expressions

• implicitly equated to 0,
• with only 1 term,
• with multiple unknown dependent functions (such as would appear in any system of DEs), 
• with no unknown dependent functions, or
• with no diff (such as may appear in a system of DAEs).

LeftRight:= proc(Q::{`=`(algebraic), algebraic})
local
    _0, 
    (L,R):= selectremove(hastype, _0 + `if`(Q::`=`, (lhs-rhs)(Q), Q), 'typefunc'(name, Not(mathfunc)))
;
    eval(`if`(L=0, R=0, L = -R), _0= 0)           
end proc
:
test_cases := <
   diff(u(x,t),t,t) + 3 + 2*diff(u(x,t),t) + 4*t + x^2 + x^3/3 
       + diff(u(x,t),t,x,x) + diff(u(x,t),x,x,x,x) = x*t^2,
   y(x) + diff(y(x),x) + cos(x) + g(y(x)) + diff(f(x),x) + 1/x = sin(x),
   diff(f(x),x) + 1/x = sin(x),
   y(x) + x,
   x*diff(y(x),x) + x = y(x) + diff(y(x),x$2),
   x^2 + 1/y(x) + diff(y(x),x) + sin(x) = y(x)^2,
   1 + x,
   diff(y(x),x)= 0,
   diff(y(x),x$2) = y(x) - x,
   sin(x)+y(x)=0
>:
<test_cases | <seq(`&nbsp;`, numelems(test_cases))> | LeftRight~(test_cases)>;

Here is a set of procedures that do what your procedure was expected to do, and do it in any base, not just base-10. For pedagogical reasons, I have not used any package commands. All commands that I use (except ifactors) are simple integer arithmetic. I did this for pedagogical reasons; I don't have anything against  the NumberTheory package. Many of my procedures duplicate functionality from NumberTheory. And their code is so arithmetically simple that I think you'll be able to learn from them. All of these procedures run in time equal to or slightly less than their NumberTheory counterparts.

Also, it seems that RepeatDecimal subpackage of NumberTheory is limited to base-10.

Download RationalPeriod.mw

Your problem comes from using the default equality operator = to check the mathematical equality of algebraic expressions, but = only checks whether the expressions are syntactically identical in their unsimplified form. That's a much stronger form of equality than mathematical equality. Use the command is to check mathematical equality. Your code should include something to do if is returns FAIL, which means that it couldn't determine mathematical equality. Here's a revision of your procedure:

Download CauchyRiemann.mw