InputField ....  name=x
and I calculate a value for the variable x:
Set V[x] .....

The first time I run the transaction the value does not appear; from the second time on, it does appear. What could be the reason?

The value is taken when the InputField statement is processed; thus you need to calculate the variable before executing the InputField statement:

Set V[x] .....

InputField ....  name=x