Simple copy-and-paste into a Maple 11 Classic 1D input line worked.   In my browser, if you right-click on the image and look at Properties you'll see there's an "Alternate Text", which explains how this works I guess.

Simple copy-and-paste into a Maple 11 Classic 1D input line worked.   In my browser, if you right-click on the image and look at Properties you'll see there's an "Alternate Text", which explains how this works I guess.

Yes, implicitplot was rewritten and greatly enhanced in Maple 11.

Ah... we generally call that "a large negative number", not "a small number".

It looks like Maple is basically adding up the hypergeometric series term by term. 
Of course with z so large (whether positive or negative) it's going to take an awful lot of terms to do that.  I have no idea what matlab does with this.  But here in Maple it's much better to use the closed-form expression

-1/2*Pi^(1/2)*(-1+erfc((-z)^(1/2)))/exp(z)/(-z)^(1/2)

or, even better, the asymptotic series of this as z -> infinity:

1/(2*z)+1/(4*z^2)+3/8/z^3+15/16/z^4+O((1/z)^(9/2))

Ah... we generally call that "a large negative number", not "a small number".

It looks like Maple is basically adding up the hypergeometric series term by term. 
Of course with z so large (whether positive or negative) it's going to take an awful lot of terms to do that.  I have no idea what matlab does with this.  But here in Maple it's much better to use the closed-form expression

-1/2*Pi^(1/2)*(-1+erfc((-z)^(1/2)))/exp(z)/(-z)^(1/2)

or, even better, the asymptotic series of this as z -> infinity:

1/(2*z)+1/(4*z^2)+3/8/z^3+15/16/z^4+O((1/z)^(9/2))

My guess is that he's talking about the question of when x^x is a rational or irrational number and/or whether it's an algebraic or transcendental number. 

Of course x^x is transcendental except for a countable set of values of x > 0, which can be enumerated as ln(y)/LambertW(ln(y)) where y is an algebraic number >= exp(-1/e)
or ln(y)/LambertW(-1,ln(y)) where y is algebraic and 1 >= y >= exp(-1/e).  Deciding whether a particular x is one of these values is not easy.

However, I might note that the Gelfond-Schneider Theorem tells us that x^x is transcendental whenever x is an irrational algebraic number.

Yes, that would be a very good idea.

I'm still having problems with this editor.  One of the problems seems to be the way the Format box does not behave as a toggle (as e.g. the bold and italic buttons do).  It seems that there's no way to switch Format in the middle of a paragraph.  It only affects the whole paragraph.  If I try switching to Formatted (to write some input code) without having a proper paragraph break, it switches the previous paragraph too. 

Try it like this:

> P:=4*(x^2+y^2-2*x)^2+((x^2-y^2)*(x-1))*(2*x-3);
   plots[implicitplot](P, x=-0.2 .. 1.5, y=-1.2 .. 1.2, grid=[50,50], gridrefine=3);

No, the code for Student:-Calculus1:-CheckExactCriticalPoints is the same in Maple 9.5 and Maple 11. 

Ah, I think I see the difference.  In Maple 9.5, CheckExactCriticalPoints is given the roots in RootOf notation, and there it's quite simple to check that they satisfy the polynomial.  In Maple 11, it gets the expressions in terms of radicals, and then it's much harder.

No, the code for Student:-Calculus1:-CheckExactCriticalPoints is the same in Maple 9.5 and Maple 11. 

Ah, I think I see the difference.  In Maple 9.5, CheckExactCriticalPoints is given the roots in RootOf notation, and there it's quite simple to check that they satisfy the polynomial.  In Maple 11, it gets the expressions in terms of radicals, and then it's much harder.

CriticalPoints must solve a quartic polynomial: that part is easy, though the results are complicated.  Then it needs to figure out which of the roots are real.   That part is OK too.  Now CriticalPoints seems to want to be extra careful (perhaps because solve is known to sometimes return spurious solutions), so  it  evaluates the derivative at each of the candidate critical points, and tries to check whether the result is 0, using signum.  That seems to be what takes forever.

CriticalPoints must solve a quartic polynomial: that part is easy, though the results are complicated.  Then it needs to figure out which of the roots are real.   That part is OK too.  Now CriticalPoints seems to want to be extra careful (perhaps because solve is known to sometimes return spurious solutions), so  it  evaluates the derivative at each of the candidate critical points, and tries to check whether the result is 0, using signum.  That seems to be what takes forever.

My understanding is that you don't need to "search for the temperature", you just give dsolve the equations that must be satisfied, including the equation PCALC = Pbar
(expressed in terms of the variables T1(t), X1(t), etc) and the initial conditions for those variables.

My understanding is that you don't need to "search for the temperature", you just give dsolve the equations that must be satisfied, including the equation PCALC = Pbar
(expressed in terms of the variables T1(t), X1(t), etc) and the initial conditions for those variables.

This looks pretty similar to the old question, with a small change of variables.  What I might do is this:

> eq1:= tan(sqrt(lambda*alpha-(alpha/2)^2))
       = -2/alpha*(sqrt(lambda*alpha-(alpha/2)^2));
   eq2:= simplify(eval(eq1,lambda=mu*alpha)) assuming alpha > 0;

(I hope I'm right in assuming alpha > 0 for your problem)

eq2 := tan(1/2*alpha*(4*mu-1)^(1/2)) = -(4*mu-1)^(1/2)

> _EnvAllSolutions:= true;
  alphaz:=solve(eq2,alpha);

alphaz := 2*(-arctan((4*mu-1)^(1/2))+Pi*_Z1)/(4*mu-1)^(1/2)

>  alpha1 := eval(alphaz, _Z1=1); lambda1 := mu*alpha1;

(_Z1 = 1 seems to give the least positive lambda for given alpha)

> plot([alpha1, lambda1, mu=0.27 .. 7.9], labels = [alpha, lambda]);