ごめんなさい、悪いです。 どうもありがとう。

I got AC now. As for the machine translate generated above, I do not actually know Japanese other than the meaning of the Kanji, but AtCoder did inspire me to more seriously learn it. xD

私は実際に日本人とあまり話したことはありませんが、そのうち話すようになるかもしれません。

from library-checker-problems.

On your implementation

I think Your implementation in atcoder/ac-library#175 is just wrong, and it is not a bug of AtCoder Library.

As writtern in the document of lazy segtree of ACL: https://github.com/atcoder/ac-library/blob/master/document_en/lazysegtree.md
$f(x\cdot y)=f(x)\cdot f(y)$ is needed. $f\colon x\mapsto x+c$ doesn't satisfy the condition.

I think the correct implementation looks like:

struct T {
  lint count, sum;
};

T op(T a, T b) { return {a.count + b.count, a.sum + b.sum}; }
T e() { return {0, 0}; }

T mapping(lint f, T x) { return {x.count, x.sum + f * x.count}; }
lint composition(lint f, lint g) { return f + g; }

We need to add $f$ to some aggregated data of a interval. If we keep only the sum, we can't find the resulted data.
By keeping both count and sum, we can get the result.

from library-checker-problems.

On the problem proposal

We can verify the lazysegtree implementation by the following problem.
https://judge.yosupo.jp/problem/range_affine_range_sum

Furthermore, range add operation is a special case of range affine operation ($b=1$).
So I think we don't need a new problem.
However, we could consider adding it if there are new algorithms that need verification and cannot be tested in the existing problem.

If some hack cases are required, it should be added to range_affine_range_sum.

from library-checker-problems.