Adding rows based on cell value & inputting values into a function

I'm having a few minor issues with my spreadsheet.
1. I don't know how to make the spreadsheet dynamically add and subtract rows based on a cell value. For example with my sheet I would like the value found in cell C4 to correspond to how many rows appear specifically up to 20. So If the value were to change to 10 I would like the spreadsheet to adapt accordingly and produce only 10 rows all across the spreadsheet from rows 9-28. I believe this would mess up my current sum function so If anyone knows what to do with that I'd appreciate it.

2. My spreadsheet in it's current state applies to only one function. With my case it is x^2. I'm lost on how to make my spreadsheet apply to any function. I'll do my best to explain what I mean. If I were to place any function into cell B1, I would like to be able to plug in values and get a solution to the function. So lets say the function in B1 changes to X+1. I would like to be able to input values from lets say cell C9 into that function and get a solution.

Any help would be greatly appreciated
Thank You
Excel Rienamm Sum.xlsx

Thanks so much for the reply but I'm not sure what to do with the yellow or green cell. I see that the yellow cell correctly indicates where the last row should be based on the value in C4. But the rows past that are still there. Is there any way to make the number of rows that appear = exactly the amount found in cell C4 ?

I will take a look. Thanks

^ I downloaded the spreadsheet and tried it out. But when I input a value in C4 for the number of intervals the amount of rows don't change.
There are still 20 rows.