...
if   ... then result := ...
elif ... then result := ...
else result := 0;
end if
...
return result

Also: use '*' and not a dot for multiplication

And note that (m*Pi) = (k*bo) is not a good idea, if working with floats.
A better way to compare is something like abs(a - b) smaller than ...

Or evalf( abs(a - b) ), because Pi is a symbol (though Maple should
take care for that here - but strictly your b0 is just a float)

With the classical interface and without re-defining that operators
I do not have a problem like that:

with(Physics):
a+b*c;
                               a + b c

Perhaps by lprint or use the classical interface - no problem there for me

For example you can use 'simplify' or 'expand'.

Why do you expect a specific answer? You may try to search for solvable polynomial equations (Google, Wikipedia) and yours is not in a form, that I would expect something good.

Or as a rule of thumb: degree beyond 4 ---> forget it, impossible by theory. Or at least a bit more precise: one can not give explicit values using radicals (guessing that you expect such) in general

And thus a Computer system will reject the task, if it can not detect a special situation.

http://en.wikipedia.org/wiki/Polynomial#Solving_polynomial_equations says a bit more (and in the links there are 'cryptic' answers saying 'yes. we can', but actually that is *generally* useless, nobody knows how to handle that).

May be you give the excat commands or upload the
essential part as a worksheet.

  restart: interface(version);

    Classic Worksheet Interface, Maple 15.01, Windows, Jun 1 2011, Build ID 635520

  sqr:= x -> x^(1/2);
                                        1/2
                           sqr := x -> x

  cp:=Compiler:-Compile(sqr):  # no problem ...

  cp(2.25);                    # and it works

                         1.50000000000000000

with(Physics);
Setup(noncommutativeprefix = z);

(z2+z1)*z1 + z2*z1;
expand(%);
% mod 2; # for the additive group 

                                   2
                                 z1

Edited: which is better recognized at the following example

(z1+z2)^2 ;              expand(%); # knows powers, cares for non-commuting
% - Commutator(z2, z1);  expand(%); # giving the usual formula
% mod 2;                            # additive modulo 2

                                2     2
                              z2  + z1

I do not know why Maple sometimes responds a bit strange,
but the following should do here:

solve((1/4*(beta^2-6))*(-beta^2+2*alpha) > 0);
convert(%, piecewise, beta);

Those empty brackets just say: not real solution.

PS: be aware that fixed fonts do not have a line break here,
so try 80 chars or less per line

The correct notation is using variables within Y:

  A := diff(     Y(x,y), y$2) - (y11)^2* diff(Y(x,y),y)   = 0;
  B := diff(diff(Y(x,y),x),y) -  y11   * diff(Y(x,y),x$2) = 0;

Please state your question more precise - it is not clear what you want.

The post "as picture" is difficult to read, may be in future you want to post
such as pdf?


Doing a lengthy numerical calculation you always will be faced rounding errors
and they even depend on the sequencing of calculation (whether you use Maple
or something else).

That also depends on working precision and you always should use at least double
precision (i.e. Digits:=15) in general.

As at a first glance I do not even see a reason why not to chose higher precision
for example Digits:=48.

That's what Preben Alsholm already said.

Note that all this will still depend on your input (which means: if your input
provides only short decimals then this may be a source for troubles as well),
so try to provide data as precise as possible.

If it is actually a problem of precise evaluation then it makes sense to convert
floating point numbers to rationals and work with that.

As Markiyan already said in http://www.mapleprimes.com/questions/134365-Eliminating-Noise,
try to understand the according help page (and it will depend on Digits used)

1e-5*h; 
fnormal(%, Digits, 1.1*1e-5);

                                  0.

Maple has a command, see the help for ?assume bottom of that page) or ?in with
some sparse explanations for 'SetOf'.

Probably you better use assume or assuming and the command ?solve or ?match, try
to have a look at some of the examples in the help.

I think that formula is only valid, if the denominator has no multiple roots
(so it is a 'generic' answer):

It is summing over all roots alpha of the denominator for the summands as

  numer(f)/diff(denom(f),x):
  subs(x=alpha, %)* 1/(x-alpha); # = constant * 1/(x-alpha)
  int(%, x);                     # = constant * log

The constant (w.r.t. variable x) however is singular, if alpha is multiple.

Following the recipe at http://eqworld.ipmnet.ru/en/solutions/lpde/lpdetoc1.htm
(download the pdf there) I get the following solution (0 < t)

U := 1/2/(t*Pi)^(1/2) * 
  Int(arctan(xi)*exp(-1/4*(x-xi)^2/t),xi = -infinity .. infinity) +1-exp(-t)

-diff(U,t)+diff(U,x,x)+exp(-t); combine(%): simplify(%);

  0


For the ic I only have numerical evidence (using small values of t and
test values for x as well), no direct proof.


However have no idea for the limit.


Edited: I am not sure, whether interchanging limit and integral is valid

  U;
  IntegrationTools[Change](%, (x-xi)/2/sqrt(t) = u,u)  assuming 0 <t;
  eval(%, arctan = 'u -> -Pi/2'); # limit x = infinity
  value(%);

    1/2*Pi+1-exp(-t)

Did it in Maple 12.

If not:

You may search the forum, if I remember correctly there was some script
or sheet (by Joe Riel?) to repair sheets.

PS: you may wish to consider to use 'clasiscal sheets', they are more easy
to handle for beginners (but would not handle Maplets)

uss_if_2_M12.mw