Write a Python function `find_element(arr, ranges, rotations, index)` that determines the element at a given index in a list after performing a series of rotations. Each rotation is defined by a range `[left, right]` (inclusive), which specifies the subarray to be rotated to the right by one position.
#### Example
```python [main.nopy]
arr = [1, 2, 3, 4, 5]
ranges = [(0, 2), (0, 3)]
rotations = 2
index = 1
result = find_element(arr, ranges, rotations, index)
print(result) # Output: 3
```
#### Constraints
- The `ranges` list will contain valid ranges within the bounds of `arr`.
- The `rotations` value will not exceed the length of the `ranges` list.
- The `index` will always be a valid index within `arr`.