Bedrock大语言模型智能解题测试

all_llms = [ model['modelId'] for model in bedrock.list_foundation_models()['modelSummaries']]
prompt_data = """小圆的半径是3cm,大圆的半径是5cm,大圆与小圆的面积比是()。
A.3:5
B.9:25
C.25:9
D.5:3"""

body = {
            "anthropic_version": "bedrock-2023-05-31",
            "max_tokens": 1024,
            "messages": [
                 {
                    "role": "user",
                    "content": [
                        {
                            "type": "text",
                            "text": prompt_data
                        }
                    ]
                }
            ],
        }

在这个问题中，我们需要找出大圆与小圆面积的比值。让我们一步步来解决：

1. 首先，我们知道圆的面积公式是：A = πr²，其中 A 是面积，r 是半径。
2. 小圆的半径是 3cm，所以小圆的面积是：

  A₁ = π(3²) = 9π cm²

3. 大圆的半径是 5cm，所以大圆的面积是：

  A₂ = π(5²) = 25π cm²

4. 现在，我们可以计算大圆与小圆面积的比值：

  A₂ : A₁ = 25π : 9π

5. 我们可以约分 π，得到：

  25 : 9

所以，正确答案是选项 B：25 : 9，也可以写作 25/9 或 2.78（保留两位小数）。

with open("images/math.png", "rb") as image_file:
    encoded_string = base64.b64encode(image_file.read())
    base64_string = encoded_string.decode('utf-8')

payload = {
    "modelId": "anthropic.claude-3-haiku-20240307-v1:0",
    "contentType": "application/json",
    "accept": "application/json",
    "body": {
        "anthropic_version": "bedrock-2023-05-31",
        "max_tokens": 1000,
        "messages": [
            {
                "role": "user",
                "content": [
                    {
                        "type": "image",
                        "source": {
                            "type": "base64",
                            "media_type": "image/png",
                            "data": base64_string
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                    },
                    {
                        "type": "text",
                        "text": "As shown in the figure, in the rectangle quadrilateral ABCD, if E is a point on the edge AB, DAE folded along the crease DE to DA'E, Please independently assess the correctness of the following three statements and provide a complete analysis: \n1. The trajectory of the projection of point A' is F, AF is perpendicular to DE;\n2. AF intersects DE at O, When E varies, the trajectory of O is a circle with AD as the diameter;\n3. The trajectory of point A' is a circle with O as the center and AO as the radius;"
                    }
                ]
            }
        ]
    }
}

Let's analyze each statement independently:

1. "The trajectory of the projection of point A' is F, AF is perpendicular to DE."
This statement is correct. As the point E moves along AB, the folding line DE also moves. The point A' is the reflection of point A across the folding line DE. By the properties of reflections, the line segment AA' is always perpendicular to the folding line DE, and its midpoint lies on DE. The trajectory of point F, which is the projection of A' onto AD, forms a line segment perpendicular to DE.

2. "AF intersects DE at O. When E varies, the trajectory of O is a circle with AD as the diameter."
This statement is correct. Let's prove it using the inscribed angle theorem. As E moves along AB, the angle ∠ADE remains a right angle (90°). Therefore, points A, D, and E always form a right triangle with ∠ADE = 90°. The point O, being the intersection of AF and DE, is the midpoint of the hypotenuse AD in this right triangle. According to the inscribed angle theorem, any angle inscribed in a semicircle is a right angle. Consequently, as E varies, the point O traces a semicircle with AD as its diameter. Since the situation is symmetrical on both sides of AD, the complete trajectory of O is a circle with AD as the diameter.

3. "The trajectory of point A' is a circle with O as the center and AO as the radius."
This statement is also correct. We can prove it using the properties of reflections. As established earlier, the point A' is always the reflection of point A across the folding line DE. Therefore, the line segment AA' is always perpendicular to DE, and DE is the perpendicular bisector of AA'. Since O is the midpoint of AD, it is also the midpoint of AA'. As E varies and DE changes, the position of A' changes accordingly, but the distance A'O remains equal to AO. Thus, the trajectory of point A' is a circle with O as the center and AO as the radius.

In conclusion, all three statements are correct, and their validity can be demonstrated using geometric principles such as the properties of reflections and the inscribed angle theorem.

prompt_data = """Because people expect theater directors to be authoritarians, many were surprised that Clark was so _____.

histrionic
megalomaniacal
egalitarian
indolent
charismatic"""

The word that best fits the blank is "egalitarian".

Egalitarian means believing in or based on the principle that all people are equal and deserve equal rights and opportunities. If Clark was egalitarian as a theater director, it suggests he treated everyone in the cast and crew as equals, rather than being an authoritarian who demanded obedience and maintained strict hierarchies.

The other options don't fit as well in the context:

- Histrionic means excessively dramatic or emotional, which doesn't directly contrast with being authoritarian.
- Megalomaniacal means having delusions of grandeur or an obsessive desire for power, which aligns more with authoritarianism than contrasts with it.
- Indolent means lazy, which isn't a clear opposite of authoritarian.
- Charismatic means charming and able to inspire devotion in others, which, while a positive trait, doesn't necessarily imply a contrast with authoritarianism.

Therefore, "egalitarian" is the best choice to fill in the blank, as it presents a leadership style that would be surprising for people who expect theater directors to be authoritarian.

最能够填补空白的词是"平等主义的"。 平等主义意味着相信或基于所有人都是平等的原则，并应该享有平等的权利和机会。如果克拉克作为一个话剧导演是平等主义者，这表明他平等地对待所有演员和工作人员，而不是一个要求服从和维持严格等级制度的权威主义者。其他选项在这个语境中就不太合适：

- 夸张的意味着过于戏剧性或情绪化，这并不能直接与权威主义形成对比。

- 偏执狂意味着幻想伟大或对权力的迷恋，这更符合权威主义而不是与之形成对比。

- 懒惰意味着懒惰，这不是权威主义的明确对立面。

- 有魅力意味着迷人并能激发他人的忠诚，尽管这是一个积极的特质，但并不一定意味着与权威主义形成对比。

因此，"平等主义的"是填补空白的最佳选择，因为它描述了一种令人意外的领导风格，相对于人们预期的话剧导演的权威主义风格。