Update the function incrementCount to accept two parameters, count and maximumCount. The function should increment count by 1 and add the incremented value to a running total. Only the incremented value should be added to the running total, not the original count.
This process should continue until the incremented count (not the running total) reaches or exceeds the maximumCount. Finally, the function must return the running total. The count should increment at least once irrespective of the maximum count.
Note: Do NOT use do..while or any other looping constructs. Use higher-order functions like map, filter, etc.