If you want to send me your notebook, or the simplest version of it - and it has all the necessary initializations so it will evaluate - maybe I can give some more explicit suggestions. My email is in my profile.

Your work might easily develop into an application - something more than just scratchpad calculations. I have an essay on my web site "A Mathematica Style" that gives information on how to organize your work this way, including using packages.

A Mathematica Style

The reason I mentioned a Module is that a Module can use temporary variables and have many statements within it. It could check parameters and issue error messages if they are not valid. If they are valid it could establish definitions for other routines you might use. All of these statements would be within the Module and not scattered through the notebook. You could have a Routines section at the top of your notebook that contained the Module routine (and other routines). Once the routine was tested you could close the Routines section so it wouldn't take a lot of space in the notebook.

I guess my first question would be: How much experience have you had with Mathematica? Have you ever written routine definitions or specifications? Have you ever used a Module or With statement? Have you ever written a usage statement or a statement that generates a Message?

Could you write a routine that checks the validity of your set of parameters? If they are not valid it might print error messages and Abort the calculation. If they are a valid set then you could complete the calculation and make a plot, although the plot would probably be another separate routine. Or maybe if the parameters are valid then the routine would establish a number of function definitions that are based on those parameters. Then further calculations would use those definition.

The object then is to partition your calculation into a number of steps, which themselves are encapsulated in routines, usually using a Module. Parameters and variables should be arguments in functions and not things that are set by separate statements in the notebook.

Cyrille, your question is a bit vague and so I don't have a good picture of what you are doing. I have a picture of you calculating something step by step with various steps in different cells and then using the result to make a plot.

If so, then one solution is to consider your work as a preliminary exploration and then trying to write a routine where the parameter you define near the top of the notebook would be a parameter in the routine definition. Then at the time you make your plot you can specify the value of the parameter, rather than specifying it at the top of the notebook.

Here is a simpler example. Suppose an ellipse with semi-axes a and b was part of your plot. Then at the top of your notebook you could define a parameterization for the ellipse. (Taken from Alfred Gray, Modern Differential Geometry)

ellipse[a_,b_][t_]:= {a Cos[t], b Sin[t]}

where a and b are the parameters in the definition. You only need to specify their values at the time you make the plot.

For a more complicated object the right hand side would probably be a Module with various steps and intermediate results.