Let $f : [0,1] \to \mathbb{R}$ be a function defined as follows: $\large f(x) = 10 x^{\sin x + \cos x}$

Enter the value of the following expression:

$\left \lfloor \int_0^1 f(x) \, dx\right \rfloor$

**Details and Assumptions:**

- $\lfloor \cdot \rfloor$ denotes the floor function.
- This question is meant to be done without computational aids.