To evaluate the expression f(1) + f(2) + f(3) + ... + f(999) + f(1000), we need to understand the behavior of the function f(x) first.

The function f(x) is defined as the floor of (2 - 3x)/(x + 3). The floor function rounds down to the nearest integer. We can observe the behavior of this function for different values of x to understand how to proceed.

Let's analyze the function for a few values of x:

f(1) = floor((-1)/4) = -1

f(2) = floor((-4)/5) = -1

f(3) = floor((-7)/6) = -2

f(4) = floor((-10)/7) = -2

f(5) = floor((-13)/8) = -2

It seems that f(x) remains constant within intervals of x before decreasing by 1 and remaining constant again.

Now let's find the length of each interval:

For x = 1 to x = 4, f(x) = -1.

For x = 5 to x = 8, f(x) = -2.

This pattern continues. So, for each interval of length 4, the value of f(x) remains constant, then decreases by 1.

The sum of all f(x) from x = 1 to x = 1000 can be calculated by dividing 1000 by 4 to find out how many complete cycles occur, and then multiplying by the sum of each cycle plus the remaining values.

Number of complete cycles: 1000/4 = 250.

In each cycle:

For x = 1 to x = 4, the sum is -1 -1 -1 -1 = -4.

For x = 5 to x = 8, the sum is -2 -2 -2 -2 = -8.

So, the sum of each complete cycle is -4 -8 = -12.

The remaining values are f(997), f(998), f(999), f(1000). These are -3, -3, -3, -3 respectively.

So, the total sum is 250 * (-12) - 12 = -3000 - 12 = -3012.