Zare,

1. Either are ok in this case, however, Sometimes you evaluate an expression that contains a variable, ie "x". and then want to create a function of x from the evaluated expression, you would use = if you want to evaluate the expression immediately.

2. You need to be a bit clever to do the dynamic number of parameters to Manipulate. Here is an example that creates at list of the variables in an expression (data) and then constructs the Manipulate that you want.

Lets create a function to get all the variables in an expression:

findAllVars[eqns_] := 
 DeleteCases[
  Union[Flatten[
    Replace[eqns , head_[args___] -> List[args], {0, Infinity}]]], 
  x_ /; NumericQ[x]]

Now we can use it in your example. I assume that "data" contains your expression -- you can also make this a function of data instead of having data being global.

With[{arr = Arrow[data], 
  varSliders = Sequence @@ Map[{#, 0, 100} &, findAllVars[data]]}, 
 Manipulate[
  Graphics3D[{arr, region}, Axes -> True, ViewPoint -> Front], 
  varSliders]]

You need a "With" to place the arrow expression into the Manipulate because Manipulate has attribute HoldAll. You need to construct a sequence to specify the slider variables to the Manipulate. Again, you need to insert the sequence using With. The Map constructs the arguments in the proper format for Manipulate.

I hope this helps.

Regards,

Neil

Zare,

Your error is because you need to quit the kernel. You defined arrows one way and I changed the way it is used in the posted code. The code I posted works with your example if you delete ShowAll code and use what I posted instead.

Regards

Zare,

Your arrows are functions of x so you need to pass the variable x to your arrows and manipulate x. Do this instead of ShowAll[]:

Module[{}, arrows[x_] = Arrow[data];
 region = 
  Point[{{0, 0, 2}, {0, 0, -2}, {0, 2, 0}, {2, 0, 0}, {0, -2, 0}, {-2,
      0, 0}}]; 
 Manipulate[
  Graphics3D[{arrows[x], region}, Axes -> True, 
   ViewPoint -> Front], {x, 0, 100}]]

Also, you should not use capital letters for your functions because they will inevitably conflict with internal Mathematica functions/Symbols.

Regards,

Neil