Count Non-Empty Substrings

Write a Python function `number_of_substrings(s: str) -> int` that calculates the number of non-empty substrings of a given string `s`.

A substring is defined as a contiguous sequence of characters within a string. For a string of length `n`, the total number of non-empty substrings can be calculated using the formula:

\[
\text{Number of substrings} = \frac{n \times (n + 1)}{2}
\]

#### Example Usage
```python [main.nopy]
print(number_of_substrings("abc"))  # Output: 6
print(number_of_substrings("abcd"))  # Output: 10
print(number_of_substrings("a"))  # Output: 1
```

#### Constraints
- The input string will have a length between 1 and 10,000.
- The function should run efficiently for large input sizes.