Write a method that calculates the total rating score for a product based on customer feedback. Each rating consists of a star value (1-5) and an influence score (1-3) indicating the customer's influence level. The method should multiply each star value by its influence score and return the sum.
Examples:
Input: stars = [4, 3, 5], influence = [2, 1, 3]
Output: 26
Explanation: (4 * 2) + (3 * 1) + (5 * 3) = 8 + 3 + 15 = 26
Input: stars = [5, 5], influence = [3, 1]
Output: 20
Explanation: (5 * 3) + (5 * 1) = 15 + 5 = 20
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