What are different types of functions in Julia and what are the differences between them?

The fs and dfs are from the sigmoidal programming library mentioned in the link earlier and they are not in my code. I just copied one of the examples in the repo and ran it on my system. That seems to work but when I do it myself, it throws up errors.
states, actions are used to define the constraints and this issue is specific to objective function, ergo they’re unrelated I guess, however, I am open to sharing entire code if that helps in any way. b is a model parameter and is between 0 to 1. So what I basically want to do is generate a list of functions with coeff[i]*x^b where I can change b at the top, where I assign different values to different parameters of the model and it would work out. Or so I think. coeff[i] is basically the cost of the associated variable.

Here is the link to my other, related question: Community post