There already are more articulate discussions of the relation between printing manuals and the environment, but just to chip in:

I plant a tree -> I create a tree.

I stop someone from cutting a tree -> I save a tree.

I refrain from cutting a tree -> I do neither of the above.

I don't know either... upload the worksheet?

 Marko, it's good practice to copy-paste your code in a copy-pasteable way, for others to quickly get to your question.

s := sum((-1)^(n+1)/(n^2+a), n=1..infinity) assuming a>0;

s := (-(1/2*I)*(1+a)*((1/2)*Psi(1/2-(1/2*I)*(I+sqrt(a)))-(1/2)*Psi(-(1/2*I)*(I+sqrt(a))))/sqrt(a)+(1/2*I)*(1+a)*((1/2)*Psi(1/2-(1/2*I)*(I-sqrt(a)))-(1/2)*Psi(-(1/2*I)*(I-sqrt(a))))/sqrt(a))/(1+a)

I am so not the expert you're looking for. Usually, convert(s,trig); would help. The assuming a>0 is important. Someone else will find a way, I'm sure. 

P.S. EDIT: Today the mapleprimes parser is changing "a greater than 0" into a0, not good. (But not always)

@acer 

What a gem ! What a great way to leave 2012! 

Are you posting these at the Applications center? great stuff, thanks for sharing.

Happy 2013 and beyond.

@acer 

What a gem ! What a great way to leave 2012! 

Are you posting these at the Applications center? great stuff, thanks for sharing.

Happy 2013 and beyond.

It would not be easy to do. You could create two separate plots that you would then combine and display together. To zoom, you can use the view [EDIT: slip of the tongue here] option, e.g. 'view' = [0..1,0..1]. To display only the curves without the axes, you can use the option 'axes' = none. To insert a plot within a plot, you can use acer's code, posted here:

EDIT: I have located acer's code:

http://www.mapleprimes.com/questions/141635-How-To-Insert-A-Plot-Into-Another-Plot#comment141636. 

@Markiyan Hirnyk 

he means that he was unable to post a comment previously but now the problem has been fixed and he will, in the future, be able to do just that.

@Markiyan Hirnyk 

he means that he was unable to post a comment previously but now the problem has been fixed and he will, in the future, be able to do just that.

you can write seq more simply, like this instead: H=[seq(0..1,0.01)]

you can write seq more simply, like this instead: H=[seq(0..1,0.01)]

solve(z^(1+I)+I=0,z);
// 1 1 \ \
exp||- - - - I| Pi|
\\ 4 4 / /

solve(z^(1+I)+I=0,z);
// 1 1 \ \
exp||- - - - I| Pi|
\\ 4 4 / /

I couldn't quite make out the question as there is missing info,

restart;

# M=[0..10], b=[-0.5..1], Du=[1..2], Sr=0.15, Sc=[0..3], Ec=(0,1), Lambda=[0.1..1], Pr=0.71
# To begin with, fix the parameters to a single value, stored in params

k1 := diff(X[1](t), t) = X[2](t);
k2 := diff(X[2](t), t) = M*(X[1](t)-1)-(2*(eta+b))*X[2](t);
k3 := diff(X[3](t), t) = X[4](t);
k4 := diff(X[4](t), t) = (2*Sc*Du*(eta+b)*X[6](t)-Du*lambda*X[5](t)-2*Pr*(eta+b)*X[4](t)-Pr*Ec*X[2](t)^2-Pr*Ec*M*(X[1](t)-1)^2)/(1-Du*Sr);
k5 := diff(X[5](t), t) = X[6](t);
k6 := diff(X[6](t), t) = (lambda*X[3](t)+2*Pr*Sr*(eta+b)*X[4](t)+Pr*Sr*Ec*X[3](t)^2+Pr*Sr*Ec*M*(X[1](t)-1)^2-2*Sc*(eta+b)*X[6](t))/(1-Du*Sr);

SYS := [k1,k2,k3,k4,k5,k6]:

INI := [ X[1](0) = 0, X[2](0) = S[1], X[3](0) = 1, X[4](0) = S[2], X[5](0) = 1, X[6](0) = S[3] ];

params := [M = 5, b = 0, Du = 1.5, Sr = 0.15, Sc = 1, Ec = 1/2, Lambda = 0.5, Pr = 0.71, eta = 1, lambda = 1, S[1] = 1, S[3] = 1 ]; # made up some values to move forward

dsolve( eval([op(SYS),op(INI)],params), 'numeric', 'output' = listprocedure);

Note that when you write proc(a,b,c) you are being explicit about the number of arguments, (a,b,c that's 3 separate arguments), and then inside the proc you are trying to handle the case where some arguments are "missing". It's probably a better approach altogether to be very general about the number of arguments that the proc can take. Joe's second example shows that you do not here need to be explicit, it gives you more flexibility.

Another approach is to specify the argument as a list, where the list could have any number of elements. My guess is that Joe's examples are superior, but by specifying a type in a procedure you get an error message if the input is of the wrong type, so that may be useful, e.g. you apply the procedure to a previous computation which returns an error rather than a list, then the error message thrown by the proc will alert you to where in your code the problem manifests itself.

f3 := proc(l::list) map(`+`,op(l)); end proc:
f3(1,1);
Error, invalid input: f3 expects its 1st argument, l, to be of type list, but received 1
f3([1,1]);

P.S. just for fun, not using "add". If it's not a good idea, Joe will tell us  ;-)

@damazz I have no idea what sort of direction Maple is headed, but my impression is that the recent developments show a desire to make Maple a pointy-clicky sort of program with pretty palettes.

Probably not what you were hoping back then when you were involved in beta testing.

Note that this is in blatant contradiction with Maple's inability to make HD plot export a simple and bug-free experience.

There are several hints about the direction Maple is headed, only hints but still telling, e.g. the development of an app for the ipad -- how many math geeks use the ipad for math? and if anyone does use a pad, is it not more likely to be android or linux based?

My impression from reading exchanges at mapleprimes is that many, if not most, of the regular users prefer the speed and simplicity of the Classic interface, do not use 2D math, do not own a mouse, would like the ability to run programs command-line style in large batches with a compiler, possibly with another interface altogether.

A typical mapleprimes exchange is a student with 0 mapleprimes votes asking why this is not producing the expected result: 2x*y and a mapleprimes expert will explain the difference between explicit and implicit multiplication and go on to recommend using 1D input rather than 2D. The student is never heard from again.

I do not have data to go by so my impression could be all wrong. I'd love to be contradicted actually.