We are given $X = 51.3$, and the expression to evaluate is:

$(306 \times X) \times (260 \times X) + \pi \times (71 \times X) \times (153 \times X)$

Let's break this down step-by-step.

Step 1: Substitute $X = 51.3$ into the expression

$(306 \times 51.3) \times (260 \times 51.3) + \pi \times (71 \times 51.3) \times (153 \times 51.3)$

Step 2: Simplify the terms

• First term: $306 \times 51.3 = 15,692.8$, and $260 \times 51.3 = 13,338$.
  Multiply these values:
  $15,692.8 \times 13,338 = 209,894,094.4$

• Second term: $71 \times 51.3 = 3,644.3$, and $153 \times 51.3 = 7,858.9$.
  Multiply these values:
  $3,644.3 \times 7,858.9 = 28,692,134.67$ Multiply this by $\pi$ (using $\pi \approx 3.1416$):
  $\pi \times 28,692,134.67 \approx 90,167,128.3$

Step 3: Add the two terms together

$209,894,094.4 + 90,167,128.3 = 300,061,222.7$

Thus, the result of the given expression is approximately:

$\boxed{300,061,222.7}$

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Would you like further explanation on any of these steps, or do you have any more questions? Here are some related questions for you:

1. How do you simplify expressions with variables like $X$?
2. What happens if we change the value of $X$ in this expression?
3. How can I calculate similar expressions involving constants like $\pi$?
4. What is the significance of the number $\pi$ in calculations like this?
5. How would the result change if we used exact values for constants instead of approximations?

Tip: When dealing with large expressions, always break them down into smaller steps to minimize errors and keep track of your calculations easily.