Big Problem but, Small solution!!

Calculus Level 4

Let \( f\) be a function on \( \mathbb{R} \to \mathbb{R} \)such that \( f(1) = 1\). If the y-intercept of the tangent at any point \( \text{P}(x,y) \) on curve \( y = f(x) \) is equal to the cube of abcissa of \( \text{P} \). Then find \( f(-3)\).

And now if ,\[ \displaystyle\int_{0}^{ f(-3) - 9} 4 \cos\frac{x}{2} . \cos{x} . \sin\frac{21x}{2} dx = \text{k} \]

Find the value of \( \text{k} + 0.111 \)

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