Use the global name :-param , with uneval quotes, in the call to foo2.

foo1 := proc( {param:={}}, $)
  foo2(':-param'=param):
end proc:

foo2 := proc( {param:={}}, $)
end proc:

foo1('param'=1);

It turns out that this works, in at least Maple 2017.2 and Maple 2018.0,

solve({exp(2*sin(t))-1=0, 0 <= t,t <= 16}, real, AllSolutions, Explicit);

         {t = 0}, {t = Pi}, {t = 2 Pi}, {t = 3 Pi}, {t = 4 Pi}, {t = 5 Pi}

AFAIK the real option is currently documented only as part of the ?solve,parametric functionality, which is for polynomial equations. So it's unclear why that extra option makes a difference for this example. There is murkiness in how solve is dealing with this extra option.

Here's one way:

Student:-Calculus1:-Roots(exp(2*sin(t))-1=0, t=0..16);

          [0, Pi, 2 Pi, 3 Pi, 4 Pi, 5 Pi]

Try closing the right-side context-panel.

You could look at some rough procedures I wrote for this kind of thing in this old posting. Those simply insert a translation of the subregion, though, and the inlined magnification window doesn't get its own axes and tickmarks.

If you really want axes and tickmarks in the magnified portion then you could try building it with an image (or an exported and reimported subplot).  See this old posting for some rough code I wrote for that. Another variant for that kind of thing is here. Newer versions of Maple allow for directly placing an image (or a subimage) on the background of a plot, and the answers in those two old postings could likely be revamped and done more cleanly now (and without any recourse to densityplot, say). Perhaps I can find time to modernize it.

@sand15 Attached is what I get when I re-execute your worksheet in Maple 2015.2 for 64bit Linux.

Tabulate_Issue_2015.2.mw

I get the legends displayed whether or not I have Tools->Options->Display->"Automatically display legends in 2-D plots" toggled. I get the legends displayed whether or not I remove the original all output from the Worksheet before re-executing. That's all as expected.

When I open your .mw file in an external editor I do see the property legendvisibility=false on the 2-D plots in the Task regions that DocumentTools:-Tabulate embeds. And when I open your .mw file in Maple 2015.2 the legends are not displayed (until I re-execute).

Your attachment is marked as Maple 2015.0. It's possible that the behavior you see is due to a bug fixed in the point-release. Do you want to try 2015.2? (The installed for that point-releasee is available for download from here.)

For a univariate problem the method=branchandbound option instructs Optimization:-Maximize to use a global optimization approach.

(Yes, this contradicts the claim given in other Answers that Optimization is only ever attempts local optimization.)

restart;
with(Optimization):
app:=x->0.14546e-1*sin(3.141592654*x)+(-1)*0.50512e-2*sin(6.283185308*x)+0.19918e-2*sin(9.424777962*x):
ex:=x->evalf(-AiryAi(2^(2/3)*x)*(5*3^(5/6)-9*AiryBi(2^(2/3))*GAMMA(2/3))/(8*AiryAi(2^(2/3))*3^(5/6)-8*AiryBi(2^(2/3))*3^(1/3))-AiryBi(2^(2/3)*x)*(9*AiryAi(2^(2/3))*GAMMA(2/3)-5*3^(1/3))/(8*AiryAi(2^(2/3))*3^(5/6)-8*AiryBi(2^(2/3))*3^(1/3))+(1/4)*x^3+3/8):

Maximize(100*(abs(app(x)-ex(x))), x = 0 .. 1);
         [0.0715496606611132, [x = 0.414027159609182]]

Maximize(100*(abs(app(x)-ex(x))), x = 0 .. 1, method=branchandbound);
          [0.183847185739178, [x = 0.923034175928753]]

As you can see, the following involves quite a bit of hand-holding.

Download pdesol_comp.mw

You forgot to use colon-minus when trying to assign to sys3.

It should be, with colon-equals,

sys3 := {de3a, de3b};

and not (as you had it, with just the equals symbol ),

sys3 = {de3a, de3b};

Also, be careful about your syntax for multplication. It's not clear from your post whether you're using 1D or 2D input.

If you're using 1D Maple Notation then make sure you enter those products like,

(x(t))*(1-.5*x(t)-.5*y(t))    # or  x(t)*(1-.5*x(t)-.5*y(t))

and not as,

(x(t))(1-.5*x(t)-.5*y(t))    # or x(t)(1-.5*x(t)-.5*y(t))

which would be parsed as function application rather than a product.

If you're using 2D Input mode then you could use either a space to denote the multiplication implicitly, or the star symbol ( * ) to denote the multiplication explicitly.

The problem is that the Maple 2016 2D Input parser is unable to interpret that use statement until after the module is created and assigned to m.

If you are using 1D Maple notation then there is no parsing problem.

If you are using 2D Input then the module creation and assignment to m has to be executed before the 2D parser starts dealing with the execution group containing the problematic use statement.

As you've discovered one workaround is to put the use statement in a seperate execution group, after the execution group that assigns the module to m. I would prefer the alternative of not using 2D Input altogether for such programming.

It looks like your version MapleV R4 directly returns the exact radical value of sin(Pi/12).

In Maple 2017.3 an (equivalent) exact radical form can be obtained using the convert command.

sin(Pi/12);

                              /1    \
                           sin|-- Pi|
                              \12   /
r:=convert(%,radical);

                        1  (1/2) / (1/2)    \
                   r := - 2      \3      - 1/
                        4                    

ee:=1/4*sqrt(6)*(1-1/3*sqrt(3));

                       1  (1/2) /    1  (1/2)\
                 ee := - 6      |1 - - 3     |
                       4        \    3       /

radnormal(r-ee);

                               0

kernelopts(version);

   Maple 2017.3, X86 64 LINUX, Sep 27 2017, Build ID 1265877

I get the exact radical result directly from MapleV R5 but not from Maple 6.

@PhilipKroon You probably would not have had that problem with write-privilege if you had instead chosen a better location for the .mla file.

The advice in another Answer here would create the new .mla (Maple Library Archive) in the first folder in `libname`. By default that is the `lib` subfolder of your full maple installation.

It is poor advice to start fooling around in that folder, IMNSHO. It's probably even worse to fool around with i/o commands in Maple while running with admin privileges.

Alternatives are to create the new .mla file in a "toolbox" folder in the right place under your home folder. That too would not require you to alter libname in subsequent sessions in order to use it.

Yet another way is to build the new .mla file in some altogether different folder that is owned by you. In order to use it subsequently you could append `libname` in Maple sessions or (just once) append to `libname` in a personal maple initialzation file.

Please let me know if you'd like details on these suggestions (I'm away from a working copy of Maple today...)

The last opened Dcocument-Block seemed to have a corrupted Input item. If I delete that problematic Input, close off the outstanding open Group, Document-Block, two Sections, and Worksheet items in the XML file then I get the following:

1._Opgaver_1.mw

You could force the tickmarks on the second axis, eg,

plots:-display(plots:-logplot(x^2-3, x = 0 .. 100),
                  axis[2]=[tickmarks=[seq(10^i=typeset(10^convert(i,name)),i=-2..5)]],
                  legendstyle = [font = [bold, "TimesNewRoman", 30], location = right],
                  thickness = 4, font = [bold, "TimesNewRoman", 30])

restart;

ans:=sum((a+k*d)^r,k=1..infinity,formal)
     -sum((a+(k+n)*d)^r,k=1..infinity,formal);

             r             a + d     r             d n + a + d
     ans := d  Zeta(0, -r, -----) - d  Zeta(0, -r, -----------)
                             d                          d

f:=r->sum((a+k*d)^r,k=1..n):
simplify(f(7)-eval(ans,r=7));

                               0