Maple gives me a null output for an equation that has a real solution.

solve(4/x^(1/3)+1=0)

The following command seems to work

solve(4/surd(x,3)+1=0)

-64

Why doesn't this have a solution over the complex numbers, when real numbers are a subset of the complex numbers. Mathematica has the same result too.

I would like to solve {x^2+y^2+z^2 = 3, x+y+z = 3} over the reals. Clearly x=1,y=1,z=1 is a solution.

Maple seems to have a hard time with this. I have tried using with(RealDomain) and various commands.

The last solution  is getting closer to the real number answer if i substitute z = 1, but then i get the strange answer { 1=1, x=1,y=1}

I tried using wolfram and it showed me the correct answer.

Rest assured, I am a strong maple fan. I sometimes use wolfram for quick and dirty solutions.

Also is there a way to turn off "with(RealDomain)", switch back to the default domain, without using 'restart'. 

When I download the help document here

https://www.maplesoft.com/support/help/maple/view.aspx?path=int%2Fdetails

I get a bug when I execute the page.

I copied pasted the last line using 1d math notation to replicate the error.

There is no addition symbol between x^2 + O(x^5)

On the help page I don't see an error. 

 I uploaded the help file   int-details_(2).mw 

I am trying to solve a vector calculus problem, find r(t) given:

a(t) = < 4t, sin t, cos(2t) > ,  v(0) = <1,0,0>  , r(0) = <0, 1, 0 >

My approach below seems kind of complicated for such a straightforward problem.  I am trying to do this without copying pasting previous results. Also there might be a recursion issue when i defined v in terms of v(t).

Question on the ditto operator, labels, and unapply, using three examples.

Example 1:

The ditto operator produces no output. Why is that? I presumed that the ditto operator is equivalent to copying pasting the last output.

Example 2:

Here the label approach seems to work, but in example three, both the ditto and label approach fails.

Example 3:

Someone earlier said that I should use unapply.

Why isn't    " v := x->% " equivalent to "v:=unapply(%,x)"

And why does the label approach fail in the vector calculus example.